@@ -270,17 +270,29 @@ static PyMemberDef union_members[] = {
         {0}
 };
 
-static PyObject *
-union_getitem(PyObject *self, PyObject *item)
+// Populate __parameters__ if needed.
+static int
+union_init_parameters(unionobject *alias)
 {
-    unionobject *alias = (unionobject *)self;
-    // Populate __parameters__ if needed.
+    int result = 0;
+    Py_BEGIN_CRITICAL_SECTION(alias);
     if (alias->parameters == NULL) {
         alias->parameters = _Py_make_parameters(alias->args);
         if (alias->parameters == NULL) {
-            return NULL;
+            result = -1;
         }
     }
+    Py_END_CRITICAL_SECTION();
+    return result;
+}
+
+static PyObject *
+union_getitem(PyObject *self, PyObject *item)
+{
+    unionobject *alias = (unionobject *)self;
+    if (union_init_parameters(alias) < 0) {
+        return NULL;
+    }
 
     PyObject *newargs = _Py_subs_parameters(self, alias->args, alias->parameters, item);
     if (newargs == NULL) {
@@ -314,11 +326,8 @@ static PyObject *
 union_parameters(PyObject *self, void *Py_UNUSED(unused))
 {
     unionobject *alias = (unionobject *)self;
-    if (alias->parameters == NULL) {
-        alias->parameters = _Py_make_parameters(alias->args);
-        if (alias->parameters == NULL) {
-            return NULL;
-        }
+    if (union_init_parameters(alias) < 0) {
+        return NULL;
     }
     return Py_NewRef(alias->parameters);
 }