diff --git a/mypy/newsemanal/semanal.py b/mypy/newsemanal/semanal.py
index 2602c3460ccf..947fb921e23b 100644
--- a/mypy/newsemanal/semanal.py
+++ b/mypy/newsemanal/semanal.py
@@ -71,7 +71,7 @@
     IntExpr, FloatExpr, UnicodeExpr, TempNode, OverloadPart,
     PlaceholderNode, COVARIANT, CONTRAVARIANT, INVARIANT,
     nongen_builtins, get_member_expr_fullname, REVEAL_TYPE,
-    REVEAL_LOCALS, is_final_node, TypedDictExpr
+    REVEAL_LOCALS, is_final_node, TypedDictExpr, type_aliases_target_versions
 )
 from mypy.tvar_scope import TypeVarScope
 from mypy.typevars import fill_typevars
@@ -3840,6 +3840,9 @@ def add_builtin_aliases(self, tree: MypyFile) -> None:
         """
         assert tree.fullname() == 'typing'
         for alias, target_name in type_aliases.items():
+            if type_aliases_target_versions[alias] > self.options.python_version:
+                # This alias is not available on this Python version.
+                continue
             name = alias.split('.')[-1]
             if name in tree.names and not isinstance(tree.names[name].node, PlaceholderNode):
                 continue
@@ -3863,7 +3866,10 @@ def add_builtin_aliases(self, tree: MypyFile) -> None:
                 self.mark_incomplete(name, tree)
             else:
                 # Test fixtures may be missing some builtin classes, which is okay.
-                pass
+                # Kill the placeholder if there is one.
+                if name in tree.names:
+                    assert isinstance(tree.names[name].node, PlaceholderNode)
+                    del tree.names[name]
 
     def lookup_fully_qualified(self, name: str) -> SymbolTableNode:
         """Lookup a fully qualified name.
diff --git a/mypy/nodes.py b/mypy/nodes.py
index b1ae7e59f523..33cbda418115 100644
--- a/mypy/nodes.py
+++ b/mypy/nodes.py
@@ -111,6 +111,19 @@ def get_column(self) -> int:
     'typing.Deque': 'collections.deque',
 }  # type: Final
 
+# This keeps track of the oldest supported Python version where the corresponding
+# alias _target_ is available.
+type_aliases_target_versions = {
+    'typing.List': (2, 7),
+    'typing.Dict': (2, 7),
+    'typing.Set': (2, 7),
+    'typing.FrozenSet': (2, 7),
+    'typing.ChainMap': (3, 3),
+    'typing.Counter': (2, 7),
+    'typing.DefaultDict': (2, 7),
+    'typing.Deque': (2, 7),
+}  # type: Final
+
 reverse_builtin_aliases = {
     'builtins.list': 'typing.List',
     'builtins.dict': 'typing.Dict',