diff --git a/jedi/inference/syntax_tree.py b/jedi/inference/syntax_tree.py
index f55ab56b..1d8b4e2e 100644
--- a/jedi/inference/syntax_tree.py
+++ b/jedi/inference/syntax_tree.py
@@ -2,6 +2,7 @@
 Functions inferring the syntax tree.
 """
 import copy
+import itertools
 
 from parso.python import tree
 
@@ -515,10 +516,20 @@ def _literals_to_types(inference_state, result):
 
 def _infer_comparison(context, left_values, operator, right_values):
     state = context.inference_state
+    if isinstance(operator, str):
+        operator_str = operator
+    else:
+        operator_str = str(operator.value)
     if not left_values or not right_values:
         # illegal slices e.g. cause left/right_result to be None
         result = (left_values or NO_VALUES) | (right_values or NO_VALUES)
         return _literals_to_types(state, result)
+    elif operator_str == "|" and all(
+        value.is_class() or value.is_compiled()
+        for value in itertools.chain(left_values, right_values)
+    ):
+        # ^^^ A naive hack for PEP 604
+        return ValueSet.from_sets((left_values, right_values))
     else:
         # I don't think there's a reasonable chance that a string
         # operation is still correct, once we pass something like six