diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index fa83cf5..c8b10ab 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -30,7 +30,7 @@ jobs:
           - python-version: "3.9"
             os: "ubuntu-latest"
             jax-version: "0.4.27"  # Keep this in sync with version in requirements.txt
-          - python-version: "3.12"
+          - python-version: "3.13"
             os: "ubuntu-latest"
             jax-version: "nightly"
 
diff --git a/chex/_src/dataclass_test.py b/chex/_src/dataclass_test.py
index 3003a9e..f981c8a 100644
--- a/chex/_src/dataclass_test.py
+++ b/chex/_src/dataclass_test.py
@@ -21,6 +21,7 @@
 import pickle
 import sys
 from typing import Any, Generic, Mapping, TypeVar
+import unittest
 
 from absl.testing import absltest
 from absl.testing import parameterized
@@ -30,7 +31,12 @@
 import cloudpickle
 import jax
 import numpy as np
-import tree
+
+# dm-tree is not compatible with Python 3.13.
+try:
+  import tree  # pylint:disable=g-import-not-at-top
+except ImportError:
+  tree = None
 
 chex_dataclass = dataclass.dataclass
 mappable_dataclass = dataclass.mappable_dataclass
@@ -209,7 +215,9 @@ def _init_testdata(self, test_type):
     self.dcls_tree_size = 18
     self.dcls_tree_size_no_dicts = 14
 
+  @unittest.skipIf(tree is None, 'dm-tree is not compatible with Python 3.13')
   def testFlattenAndUnflatten(self, test_type):
+    assert tree is not None
     self._init_testdata(test_type)
 
     self.assertEqual(self.dcls_flattened, tree.flatten(self.dcls_with_map))
@@ -223,21 +231,27 @@ def testFlattenAndUnflatten(self, test_type):
     self.assertEqual(dataclass_in_seq,
                      tree.unflatten_as(dataclass_in_seq, dataclass_in_seq_flat))
 
+  @unittest.skipIf(tree is None, 'dm-tree is not compatible with Python 3.13')
   def testFlattenUpTo(self, test_type):
+    assert tree is not None
     self._init_testdata(test_type)
     structure = copy.copy(self.dcls_with_map)
     structure.k_dclass_with_map = None  # Do not flatten 'k_dclass_with_map'
     self.assertEqual(self.dcls_flattened_up_to,
                      tree.flatten_up_to(structure, self.dcls_with_map))
 
+  @unittest.skipIf(tree is None, 'dm-tree is not compatible with Python 3.13')
   def testFlattenWithPath(self, test_type):
+    assert tree is not None
     self._init_testdata(test_type)
 
     self.assertEqual(
         tree.flatten_with_path(self.dcls_with_map),
         self.dcls_flattened_with_path)
 
+  @unittest.skipIf(tree is None, 'dm-tree is not compatible with Python 3.13')
   def testFlattenWithPathUpTo(self, test_type):
+    assert tree is not None
     self._init_testdata(test_type)
     structure = copy.copy(self.dcls_with_map)
     structure.k_dclass_with_map = None  # Do not flatten 'k_dclass_with_map'
@@ -245,7 +259,9 @@ def testFlattenWithPathUpTo(self, test_type):
         tree.flatten_with_path_up_to(structure, self.dcls_with_map),
         self.dcls_flattened_with_path_up_to)
 
+  @unittest.skipIf(tree is None, 'dm-tree is not compatible with Python 3.13')
   def testMapStructure(self, test_type):
+    assert tree is not None
     self._init_testdata(test_type)
 
     add_one_to_ints_fn = lambda x: x + 1 if isinstance(x, int) else x
@@ -256,7 +272,9 @@ def testMapStructure(self, test_type):
                      self.dcls_with_map_inc_ints.k_int * 10)
     self.assertEqual(mapped_inc_ints.k_non_init, mapped_inc_ints.k_int * 10)
 
+  @unittest.skipIf(tree is None, 'dm-tree is not compatible with Python 3.13')
   def testMapStructureUpTo(self, test_type):
+    assert tree is not None
     self._init_testdata(test_type)
 
     structure = copy.copy(self.dcls_with_map)
@@ -273,7 +291,9 @@ def testMapStructureUpTo(self, test_type):
                      self.dcls_with_map_inc_ints.k_int * 10)
     self.assertEqual(mapped_inc_ints.k_non_init, mapped_inc_ints.k_int * 10)
 
+  @unittest.skipIf(tree is None, 'dm-tree is not compatible with Python 3.13')
   def testMapStructureWithPath(self, test_type):
+    assert tree is not None
     self._init_testdata(test_type)
 
     add_one_to_ints_fn = lambda path, x: x + 1 if isinstance(x, int) else x
@@ -285,7 +305,9 @@ def testMapStructureWithPath(self, test_type):
                      self.dcls_with_map_inc_ints.k_int * 10)
     self.assertEqual(mapped_inc_ints.k_non_init, mapped_inc_ints.k_int * 10)
 
+  @unittest.skipIf(tree is None, 'dm-tree is not compatible with Python 3.13')
   def testMapStructureWithPathUpTo(self, test_type):
+    assert tree is not None
     self._init_testdata(test_type)
 
     structure = copy.copy(self.dcls_with_map)
@@ -303,7 +325,9 @@ def testMapStructureWithPathUpTo(self, test_type):
                      self.dcls_with_map_inc_ints.k_int * 10)
     self.assertEqual(mapped_inc_ints.k_non_init, mapped_inc_ints.k_int * 10)
 
+  @unittest.skipIf(tree is None, 'dm-tree is not compatible with Python 3.13')
   def testTraverse(self, test_type):
+    assert tree is not None
     self._init_testdata(test_type)
 
     visited = []
@@ -358,7 +382,7 @@ def test_tree_flatten_with_keys(self):
     )
     leaves = [l for _, l in keys_and_leaves]
     new_obj = treedef.unflatten(leaves)
-    self.assertEqual(new_obj, obj)
+    asserts.assert_trees_all_equal(new_obj, obj)
 
   def test_tree_map_with_keys(self):
     obj = dummy_dataclass()
diff --git a/requirements/requirements-test.txt b/requirements/requirements-test.txt
index c5923a7..035bfac 100644
--- a/requirements/requirements-test.txt
+++ b/requirements/requirements-test.txt
@@ -1,2 +1,3 @@
 cloudpickle==2.2.0
-dm-tree>=0.1.5
+# dm-tree is not compatible with Python 3.13.
+dm-tree>=0.1.5; python_version < "3.13"