diff --git a/Misc/NEWS.d/next/Core and Builtins/2019-04-13-16-14-16.bpo-36601.mIgS7t.rst b/Misc/NEWS.d/next/Core and Builtins/2019-04-13-16-14-16.bpo-36601.mIgS7t.rst
new file mode 100644
index 00000000000..0159aae65d7
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2019-04-13-16-14-16.bpo-36601.mIgS7t.rst	
@@ -0,0 +1,2 @@
+A long-since-meaningless check for ``getpid() == main_pid`` was removed
+from Python's internal C signal handler.
diff --git a/Modules/signalmodule.c b/Modules/signalmodule.c
index 8c5a0d044ab..43a4da1a627 100644
--- a/Modules/signalmodule.c
+++ b/Modules/signalmodule.c
@@ -73,11 +73,12 @@ class sigset_t_converter(CConverter):
 /*
    NOTES ON THE INTERACTION BETWEEN SIGNALS AND THREADS
 
-   When threads are supported, we want the following semantics:
+   We want the following semantics:
 
    - only the main thread can set a signal handler
+   - only the main thread runs the signal handler
+   - signals can be delivered to any thread
    - any thread can get a signal handler
-   - signals are only delivered to the main thread
 
    I.e. we don't support "synchronous signals" like SIGFPE (catching
    this doesn't make much sense in Python anyway) nor do we support
@@ -88,17 +89,17 @@ class sigset_t_converter(CConverter):
    We still have the problem that in some implementations signals
    generated by the keyboard (e.g. SIGINT) are delivered to all
    threads (e.g. SGI), while in others (e.g. Solaris) such signals are
-   delivered to one random thread (an intermediate possibility would
-   be to deliver it to the main thread -- POSIX?).  For now, we have
-   a working implementation that works in all three cases -- the
-   handler ignores signals if getpid() isn't the same as in the main
-   thread.  XXX This is a hack.
+   delivered to one random thread. On Linux, signals are delivered to
+   the main thread (unless the main thread is blocking the signal, for
+   example because it's already handling the same signal).  Since we
+   allow signals to be delivered to any thread, this works fine. The
+   only oddity is that the thread executing the Python signal handler
+   may not be the thread that received the signal.
 */
 
 #include <sys/types.h> /* For pid_t */
 #include "pythread.h"
 static unsigned long main_thread;
-static pid_t main_pid;
 static PyInterpreterState *main_interp;
 
 static volatile struct {
@@ -326,11 +327,7 @@ signal_handler(int sig_num)
 {
     int save_errno = errno;
 
-    /* See NOTES section above */
-    if (getpid() == main_pid)
-    {
-        trip_signal(sig_num);
-    }
+    trip_signal(sig_num);
 
 #ifndef HAVE_SIGACTION
 #ifdef SIGCHLD
@@ -1328,7 +1325,6 @@ PyInit__signal(void)
     int i;
 
     main_thread = PyThread_get_thread_ident();
-    main_pid = getpid();
     main_interp = _PyInterpreterState_Get();
 
     /* Create the module and add the functions */
@@ -1739,7 +1735,6 @@ _PySignal_AfterFork(void)
      * the interpreter had an opportunity to call the handlers.  issue9535. */
     _clear_pending_signals();
     main_thread = PyThread_get_thread_ident();
-    main_pid = getpid();
     main_interp = _PyInterpreterState_Get();
 }