diff --git a/CHANGES.md b/CHANGES.md
index e5f4a1fdf82..5d89c71f580 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -19,6 +19,7 @@
 - Add `flake8-simplify` and `flake8-comprehensions` plugins (#2653)
 - Fix determination of f-string expression spans (#2654)
 - Fix parser error location on invalid syntax in a `match` statement (#2649)
+- Fix bad formatting of error messages about EOF in multi-line statements (#2343)
 - Functions and classes in blocks now have more consistent surrounding spacing (#2472)
 
 ## 21.11b1
diff --git a/src/black/parsing.py b/src/black/parsing.py
index e38405637cd..b673027022f 100644
--- a/src/black/parsing.py
+++ b/src/black/parsing.py
@@ -17,6 +17,7 @@
 from blib2to3.pgen2 import driver
 from blib2to3.pgen2.grammar import Grammar
 from blib2to3.pgen2.parse import ParseError
+from blib2to3.pgen2.tokenize import TokenError
 
 from black.mode import TargetVersion, Feature, supports_feature
 from black.nodes import syms
@@ -109,6 +110,12 @@ def lib2to3_parse(src_txt: str, target_versions: Iterable[TargetVersion] = ()) -
             except IndexError:
                 faulty_line = "<line number missing in source>"
             exc = InvalidInput(f"Cannot parse: {lineno}:{column}: {faulty_line}")
+
+        except TokenError as te:
+            # In edge cases these are raised; and typically don't have a "faulty_line".
+            lineno, column = te.args[1]
+            exc = InvalidInput(f"Cannot parse: {lineno}:{column}: {te.args[0]}")
+
     else:
         raise exc from None
 
diff --git a/tests/test_black.py b/tests/test_black.py
index 51a20307e56..92598532e2c 100644
--- a/tests/test_black.py
+++ b/tests/test_black.py
@@ -1557,6 +1557,15 @@ def test_code_option_parent_config(self) -> None:
                     call_args[0].lower() == str(pyproject_path).lower()
                 ), "Incorrect config loaded."
 
+    def test_for_handled_unexpected_eof_error(self) -> None:
+        """
+        Test that an unexpected EOF SyntaxError is nicely presented.
+        """
+        with pytest.raises(black.parsing.InvalidInput) as exc_info:
+            black.lib2to3_parse("print(", {})
+
+        exc_info.match("Cannot parse: 2:0: EOF in multi-line statement")
+
 
 class TestCaching:
     def test_cache_broken_file(self) -> None: