diff --git a/Include/internal/pycore_pystate.h b/Include/internal/pycore_pystate.h
index 0cd5550cfda..da6b87bd0f8 100644
--- a/Include/internal/pycore_pystate.h
+++ b/Include/internal/pycore_pystate.h
@@ -53,6 +53,22 @@ _Py_ThreadCanHandlePendingCalls(void)
 PyAPI_FUNC(PyThreadState*) _PyThreadState_GetTSS(void);
 #endif
 
+
+// Thread local storage for the current interpreter and the current Python
+// thread state, if supported by the compiler.
+#ifdef HAVE__THREAD_LOCAL_KEYWORD
+// C11 _Thread_local keyword
+#  define _Py_HAVE_TSS_TSTATE
+PyAPI_DATA(_Thread_local PyInterpreterState*) _Py_current_interp;
+PyAPI_DATA(_Thread_local PyThreadState*) _Py_current_tstate;
+#elif defined(__GNUC__) || defined(__clang__)
+// GCC and clang __thread extension
+#  define _Py_HAVE_TSS_TSTATE
+PyAPI_DATA(__thread PyInterpreterState*) _Py_current_interp;
+PyAPI_DATA(__thread PyThreadState*) _Py_current_tstate;
+#endif
+
+
 static inline PyThreadState*
 _PyRuntimeState_GetThreadState(_PyRuntimeState *runtime)
 {
@@ -75,7 +91,9 @@ _PyRuntimeState_GetThreadState(_PyRuntimeState *runtime)
 static inline PyThreadState*
 _PyThreadState_GET(void)
 {
-#ifdef EXPERIMENTAL_ISOLATED_SUBINTERPRETERS
+#ifdef _Py_HAVE_TSS_TSTATE
+    return _Py_current_tstate;
+#elif defined(EXPERIMENTAL_ISOLATED_SUBINTERPRETERS)
     return _PyThreadState_GetTSS();
 #else
     return _PyRuntimeState_GetThreadState(&_PyRuntime);
@@ -110,11 +128,15 @@ _Py_EnsureFuncTstateNotNULL(const char *func, PyThreadState *tstate)
    See also _PyInterpreterState_Get()
    and _PyGILState_GetInterpreterStateUnsafe(). */
 static inline PyInterpreterState* _PyInterpreterState_GET(void) {
+#ifdef _Py_HAVE_TSS_TSTATE
+    return _Py_current_interp;
+#else
     PyThreadState *tstate = _PyThreadState_GET();
 #ifdef Py_DEBUG
     _Py_EnsureTstateNotNULL(tstate);
 #endif
     return tstate->interp;
+#endif
 }
 
 
diff --git a/Misc/NEWS.d/next/Core and Builtins/2020-12-28-15-58-13.bpo-40522.Q5jhgq.rst b/Misc/NEWS.d/next/Core and Builtins/2020-12-28-15-58-13.bpo-40522.Q5jhgq.rst
new file mode 100644
index 00000000000..6fef4fd402e
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2020-12-28-15-58-13.bpo-40522.Q5jhgq.rst	
@@ -0,0 +1,2 @@
+If Python is built with GCC or clang, the current interpreter and the current
+Python thread state are now stored in a Thread Local Storage.
diff --git a/Python/pystate.c b/Python/pystate.c
index c791b239993..5fd1fbc5b96 100644
--- a/Python/pystate.c
+++ b/Python/pystate.c
@@ -36,9 +36,16 @@ extern "C" {
 
 #define _PyRuntimeGILState_GetThreadState(gilstate) \
     ((PyThreadState*)_Py_atomic_load_relaxed(&(gilstate)->tstate_current))
-#define _PyRuntimeGILState_SetThreadState(gilstate, value) \
-    _Py_atomic_store_relaxed(&(gilstate)->tstate_current, \
-                             (uintptr_t)(value))
+
+
+#ifdef HAVE__THREAD_LOCAL_KEYWORD
+_Thread_local PyInterpreterState *_Py_current_interp = NULL;
+_Thread_local PyThreadState *_Py_current_tstate = NULL;
+#elif defined(__GNUC__) || defined(__clang__)
+#  define _Py_HAVE_TSS_TSTATE
+__thread PyInterpreterState *_Py_current_interp = NULL;
+__thread PyThreadState *_Py_current_tstate = NULL;
+#endif
 
 /* Forward declarations */
 static PyThreadState *_PyGILState_GetThisThreadState(struct _gilstate_runtime_state *gilstate);
@@ -603,6 +610,22 @@ PyInterpreterState_GetDict(PyInterpreterState *interp)
     return interp->dict;
 }
 
+
+static void
+set_current_tstate(struct _gilstate_runtime_state *gilstate,
+                   PyThreadState *tstate)
+{
+#ifdef _Py_HAVE_TSS_TSTATE
+    _Py_current_tstate = tstate;
+    _Py_current_interp = tstate ? tstate->interp : NULL;
+#endif
+#ifdef EXPERIMENTAL_ISOLATED_SUBINTERPRETERS
+    PyThread_tss_set(&gilstate->autoTSSkey, tstate);
+#endif
+    _Py_atomic_store_relaxed(&gilstate->tstate_current, (uintptr_t)tstate);
+}
+
+
 static PyThreadState *
 new_threadstate(PyInterpreterState *interp, int init)
 {
@@ -929,7 +952,7 @@ _PyThreadState_DeleteCurrent(PyThreadState *tstate)
     _Py_EnsureTstateNotNULL(tstate);
     struct _gilstate_runtime_state *gilstate = &tstate->interp->runtime->gilstate;
     tstate_delete_common(tstate, gilstate);
-    _PyRuntimeGILState_SetThreadState(gilstate, NULL);
+    set_current_tstate(gilstate, NULL);
     _PyEval_ReleaseLock(tstate);
     PyMem_RawFree(tstate);
 }
@@ -1018,7 +1041,8 @@ _PyThreadState_Swap(struct _gilstate_runtime_state *gilstate, PyThreadState *new
     PyThreadState *oldts = _PyRuntimeGILState_GetThreadState(gilstate);
 #endif
 
-    _PyRuntimeGILState_SetThreadState(gilstate, newts);
+    set_current_tstate(gilstate, newts);
+
     /* It should not be possible for more than one thread state
        to be used for a thread.  Check this the best we can in debug
        builds.
@@ -1034,9 +1058,6 @@ _PyThreadState_Swap(struct _gilstate_runtime_state *gilstate, PyThreadState *new
             Py_FatalError("Invalid thread state for this thread");
         errno = err;
     }
-#endif
-#ifdef EXPERIMENTAL_ISOLATED_SUBINTERPRETERS
-    PyThread_tss_set(&gilstate->autoTSSkey, newts);
 #endif
     return oldts;
 }
diff --git a/configure b/configure
index 530c04a0ede..48dc8844eda 100755
--- a/configure
+++ b/configure
@@ -17129,6 +17129,37 @@ $as_echo "#define HAVE_BUILTIN_ATOMIC 1" >>confdefs.h
 
 fi
 
+# Check for _Thread_local keyword
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for _Thread_local keyword" >&5
+$as_echo_n "checking for _Thread_local keyword... " >&6; }
+cat confdefs.h - <<_ACEOF >conftest.$ac_ext
+/* end confdefs.h.  */
+
+
+    _Thread_local int val;
+    int main() {
+      val = 1;
+      return val;
+    }
+
+
+_ACEOF
+if ac_fn_c_try_link "$LINENO"; then :
+  have__thread_local_keyword=yes
+else
+  have__thread_local_keyword=no
+fi
+rm -f core conftest.err conftest.$ac_objext \
+    conftest$ac_exeext conftest.$ac_ext
+{ $as_echo "$as_me:${as_lineno-$LINENO}: result: $have__thread_local_keyword" >&5
+$as_echo "$have__thread_local_keyword" >&6; }
+
+if test "$have__thread_local_keyword" = yes; then
+
+$as_echo "#define HAVE__THREAD_LOCAL_KEYWORD 1" >>confdefs.h
+
+fi
+
 # ensurepip option
 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for ensurepip" >&5
 $as_echo_n "checking for ensurepip... " >&6; }
diff --git a/configure.ac b/configure.ac
index 39eadfedfba..d496860db00 100644
--- a/configure.ac
+++ b/configure.ac
@@ -5606,6 +5606,24 @@ if test "$have_builtin_atomic" = yes; then
     AC_DEFINE(HAVE_BUILTIN_ATOMIC, 1, [Has builtin __atomic_load_n() and __atomic_store_n() functions])
 fi
 
+# Check for _Thread_local keyword
+AC_MSG_CHECKING(for _Thread_local keyword)
+AC_LINK_IFELSE(
+[
+  AC_LANG_SOURCE([[
+    _Thread_local int val;
+    int main() {
+      val = 1;
+      return val;
+    }
+  ]])
+],[have__thread_local_keyword=yes],[have__thread_local_keyword=no])
+AC_MSG_RESULT($have__thread_local_keyword)
+
+if test "$have__thread_local_keyword" = yes; then
+    AC_DEFINE(HAVE__THREAD_LOCAL_KEYWORD, 1, [Has C11 _Thread_local keyword])
+fi
+
 # ensurepip option
 AC_MSG_CHECKING(for ensurepip)
 AC_ARG_WITH(ensurepip,
diff --git a/pyconfig.h.in b/pyconfig.h.in
index 045cbd53aee..1c10e562cb5 100644
--- a/pyconfig.h.in
+++ b/pyconfig.h.in
@@ -1359,6 +1359,9 @@
 /* Define to 1 if you have the `_getpty' function. */
 #undef HAVE__GETPTY
 
+/* Has C11 _Thread_local keyword */
+#undef HAVE__THREAD_LOCAL_KEYWORD
+
 /* Define to 1 if `major', `minor', and `makedev' are declared in <mkdev.h>.
    */
 #undef MAJOR_IN_MKDEV