diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index e6ecdd7..38f6fe2 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -3,6 +3,12 @@ Version history
 
 This library adheres to `Semantic Versioning 2.0 <https://semver.org/#semantic-versioning-200>`_.
 
+**UNRELEASED**
+
+- Fixed regression where ``Literal`` inside a ``Union`` had quotes stripped from its
+  contents, thus typically causing ``NameError`` to be raised when run
+  (`#372 <https://github.com/agronholm/typeguard/issues/372>`_)
+
 **4.0.1** (2023-07-27)
 
 - Fixed handling of ``typing_extensions.Literal`` on Python 3.8 and 3.9 when
diff --git a/src/typeguard/_transformer.py b/src/typeguard/_transformer.py
index 32d284e..d9d692d 100644
--- a/src/typeguard/_transformer.py
+++ b/src/typeguard/_transformer.py
@@ -363,6 +363,12 @@ def visit(self, node: AST) -> Any:
 
         return new_node
 
+    def generic_visit(self, node: AST) -> AST:
+        if isinstance(node, expr) and self._memo.name_matches(node, *literal_names):
+            return node
+
+        return super().generic_visit(node)
+
     def visit_BinOp(self, node: BinOp) -> Any:
         self.generic_visit(node)
 
@@ -395,7 +401,7 @@ def visit_Subscript(self, node: Subscript) -> Any:
 
         # The subscript of typing(_extensions).Literal can be any arbitrary string, so
         # don't try to evaluate it as code
-        if not self._memo.name_matches(node.value, *literal_names) and node.slice:
+        if node.slice:
             if isinstance(node.slice, Index):
                 # Python 3.7 and 3.8
                 slice_value = node.slice.value  # type: ignore[attr-defined]
diff --git a/tests/dummymodule.py b/tests/dummymodule.py
index 4f3b7ae..36aa4a4 100644
--- a/tests/dummymodule.py
+++ b/tests/dummymodule.py
@@ -333,6 +333,12 @@ def literal(x: Literal["foo"]) -> Literal["foo"]:
     return y
 
 
+@typechecked
+def literal_in_union(x: Union[Literal["foo"],]) -> Literal["foo"]:
+    y: Literal["foo"] = x
+    return y
+
+
 @typechecked
 def typevar_forwardref(x: Type[T]) -> T:
     return x()
diff --git a/tests/test_instrumentation.py b/tests/test_instrumentation.py
index 27939ad..c75f841 100644
--- a/tests/test_instrumentation.py
+++ b/tests/test_instrumentation.py
@@ -324,6 +324,11 @@ def test_literal(dummymodule):
     assert dummymodule.literal("foo") == "foo"
 
 
+def test_literal_in_union(dummymodule):
+    """Regression test for #372."""
+    assert dummymodule.literal_in_union("foo") == "foo"
+
+
 def test_typevar_forwardref(dummymodule):
     instance = dummymodule.typevar_forwardref(dummymodule.DummyClass)
     assert isinstance(instance, dummymodule.DummyClass)