diff --git a/chalice/config.py b/chalice/config.py
index dbd5dce04..f27d79d12 100644
--- a/chalice/config.py
+++ b/chalice/config.py
@@ -163,7 +163,15 @@ def lambda_python_version(self):
             return 'python3.6'
         elif (major, minor) <= (3, 7):
             return 'python3.7'
-        return 'python3.8'
+        elif (major, minor) <= (3, 8):
+            return 'python3.8'
+        elif (major, minor) <= (3, 9):
+            return 'python3.9'
+        elif (major, minor) <= (3, 10):
+            return 'python3.10'
+        elif (major, minor) <= (3, 11):
+            return 'python3.11'
+        return 'python3.12'
 
     @property
     def layers(self):
diff --git a/chalice/deploy/packager.py b/chalice/deploy/packager.py
index b2ccce979..dd29f02fc 100644
--- a/chalice/deploy/packager.py
+++ b/chalice/deploy/packager.py
@@ -77,6 +77,10 @@ class BaseLambdaDeploymentPackager(object):
         'python3.6': 'cp36m',
         'python3.7': 'cp37m',
         'python3.8': 'cp38',
+        'python3.9': 'cp39',
+        'python3.10': 'cp310',
+        'python3.11': 'cp311',
+        'python3.12': 'cp312',
     }
 
     def __init__(self, osutils, dependency_builder, ui):
diff --git a/chalice/package.py b/chalice/package.py
index 6d3e12a9a..dd0ed2aab 100644
--- a/chalice/package.py
+++ b/chalice/package.py
@@ -735,7 +735,7 @@ def _add_domain_name(self, resource, template):
                 'DomainName': {'Ref': 'ApiGatewayCustomDomain'},
                 'RestApiId': {'Ref': 'RestAPI'},
                 'BasePath': domain_name.api_mapping.mount_path,
-                'Stage': resource.api_gateway_stage,
+                'Stage': {'Ref': 'RestAPI.Stage'},
             }
         }
 
diff --git a/tests/unit/test_package.py b/tests/unit/test_package.py
index fd3c89f88..0516e9ed6 100644
--- a/tests/unit/test_package.py
+++ b/tests/unit/test_package.py
@@ -1646,7 +1646,7 @@ def test_can_generate_custom_domain_name(self, sample_app):
             'Properties': {
                 'DomainName': {'Ref': 'ApiGatewayCustomDomain'},
                 'RestApiId': {'Ref': 'RestAPI'},
-                'Stage': config.api_gateway_stage,
+                'Stage':  {'Ref': 'RestAPI.Stage'},
                 'BasePath': '(none)',
             }
         }
@@ -1680,7 +1680,7 @@ def test_can_generate_domain_for_regional_endpoint(self, sample_app):
             'Properties': {
                 'DomainName': {'Ref': 'ApiGatewayCustomDomain'},
                 'RestApiId': {'Ref': 'RestAPI'},
-                'Stage': config.api_gateway_stage,
+                'Stage':  {'Ref': 'RestAPI.Stage'},
                 'BasePath': '(none)',
             }
         }