diff --git a/Include/errcode.h b/Include/errcode.h
index 8d44e9ae559..dac5cf068c9 100644
--- a/Include/errcode.h
+++ b/Include/errcode.h
@@ -19,24 +19,25 @@
 extern "C" {
 #endif
 
-#define E_OK            10      /* No error */
-#define E_EOF           11      /* End Of File */
-#define E_INTR          12      /* Interrupted */
-#define E_TOKEN         13      /* Bad token */
-#define E_SYNTAX        14      /* Syntax error */
-#define E_NOMEM         15      /* Ran out of memory */
-#define E_DONE          16      /* Parsing complete */
-#define E_ERROR         17      /* Execution error */
-#define E_TABSPACE      18      /* Inconsistent mixing of tabs and spaces */
-#define E_OVERFLOW      19      /* Node had too many children */
-#define E_TOODEEP       20      /* Too many indentation levels */
-#define E_DEDENT        21      /* No matching outer block for dedent */
-#define E_DECODE        22      /* Error in decoding into Unicode */
-#define E_EOFS          23      /* EOF in triple-quoted string */
-#define E_EOLS          24      /* EOL in single-quoted string */
-#define E_LINECONT      25      /* Unexpected characters after a line continuation */
-#define E_BADSINGLE     27      /* Ill-formed single statement input */
-#define E_INTERACT_STOP 28      /* Interactive mode stopped tokenization */
+#define E_OK             10      /* No error */
+#define E_EOF            11      /* End Of File */
+#define E_INTR           12      /* Interrupted */
+#define E_TOKEN          13      /* Bad token */
+#define E_SYNTAX         14      /* Syntax error */
+#define E_NOMEM          15      /* Ran out of memory */
+#define E_DONE           16      /* Parsing complete */
+#define E_ERROR          17      /* Execution error */
+#define E_TABSPACE       18      /* Inconsistent mixing of tabs and spaces */
+#define E_OVERFLOW       19      /* Node had too many children */
+#define E_TOODEEP        20      /* Too many indentation levels */
+#define E_DEDENT         21      /* No matching outer block for dedent */
+#define E_DECODE         22      /* Error in decoding into Unicode */
+#define E_EOFS           23      /* EOF in triple-quoted string */
+#define E_EOLS           24      /* EOL in single-quoted string */
+#define E_LINECONT       25      /* Unexpected characters after a line continuation */
+#define E_BADSINGLE      27      /* Ill-formed single statement input */
+#define E_INTERACT_STOP  28      /* Interactive mode stopped tokenization */
+#define E_COLUMNOVERFLOW 29      /* Column offset overflow */
 
 #ifdef __cplusplus
 }
diff --git a/Lib/test/test_exceptions.py b/Lib/test/test_exceptions.py
index eafa7d84638..4031c5ca76c 100644
--- a/Lib/test/test_exceptions.py
+++ b/Lib/test/test_exceptions.py
@@ -18,6 +18,12 @@ from test.support.os_helper import TESTFN, unlink
 from test.support.warnings_helper import check_warnings
 from test import support
 
+try:
+    from _testcapi import INT_MAX
+except ImportError:
+    INT_MAX = 2**31 - 1
+
+
 
 class NaiveException(Exception):
     def __init__(self, x):
@@ -318,11 +324,13 @@ class ExceptionTests(unittest.TestCase):
         check('(yield i) = 2', 1, 2)
         check('def f(*):\n  pass', 1, 7)
 
+    @unittest.skipIf(INT_MAX >= sys.maxsize, "Downcasting to int is safe for col_offset")
     @support.requires_resource('cpu')
-    @support.bigmemtest(support._2G, memuse=1.5)
-    def testMemoryErrorBigSource(self, _size):
-        with self.assertRaises(OverflowError):
-            exec(f"if True:\n {' ' * 2**31}print('hello world')")
+    @support.bigmemtest(INT_MAX, memuse=2, dry_run=False)
+    def testMemoryErrorBigSource(self, size):
+        src = b"if True:\n%*s" % (size, b"pass")
+        with self.assertRaisesRegex(OverflowError, "Parser column offset overflow"):
+            compile(src, '<fragment>', 'exec')
 
     @cpython_only
     def testSettingException(self):
diff --git a/Parser/lexer/lexer.c b/Parser/lexer/lexer.c
index c7134ab868b..1a01bb0352a 100644
--- a/Parser/lexer/lexer.c
+++ b/Parser/lexer/lexer.c
@@ -59,6 +59,10 @@ tok_nextc(struct tok_state *tok)
     int rc;
     for (;;) {
         if (tok->cur != tok->inp) {
+            if ((unsigned int) tok->col_offset >= (unsigned int) INT_MAX) {
+                tok->done = E_COLUMNOVERFLOW;
+                return EOF;
+            }
             tok->col_offset++;
             return Py_CHARMASK(*tok->cur++); /* Fast path */
         }
diff --git a/Parser/pegen_errors.c b/Parser/pegen_errors.c
index 15e99e23d84..057bf551519 100644
--- a/Parser/pegen_errors.c
+++ b/Parser/pegen_errors.c
@@ -68,6 +68,7 @@ _Pypegen_tokenizer_error(Parser *p)
     const char *msg = NULL;
     PyObject* errtype = PyExc_SyntaxError;
     Py_ssize_t col_offset = -1;
+    p->error_indicator = 1;
     switch (p->tok->done) {
         case E_TOKEN:
             msg = "invalid token";
@@ -103,6 +104,10 @@ _Pypegen_tokenizer_error(Parser *p)
             msg = "unexpected character after line continuation character";
             break;
         }
+        case E_COLUMNOVERFLOW:
+            PyErr_SetString(PyExc_OverflowError,
+                    "Parser column offset overflow - source line is too big");
+            return -1;
         default:
             msg = "unknown parsing error";
     }