diff --git a/icechunk-python/tests/test_zarr/test_stateful.py b/icechunk-python/tests/test_zarr/test_stateful.py
new file mode 100644
index 00000000..870554fb
--- /dev/null
+++ b/icechunk-python/tests/test_zarr/test_stateful.py
@@ -0,0 +1,64 @@
+from typing import Any
+
+import hypothesis.strategies as st
+import numpy as np
+import pytest
+from hypothesis import assume
+from hypothesis.stateful import (
+    Settings,
+    rule,
+    run_state_machine_as_test,
+)
+
+from icechunk import IcechunkStore, StorageConfig
+from zarr.testing.stateful import ZarrHierarchyStateMachine, ZarrStoreStateMachine
+from zarr.testing.strategies import (
+    node_names,
+    np_array_and_chunks,
+    numpy_arrays,
+)
+
+
+class ModifiedZarrHierarchyStateMachine(ZarrHierarchyStateMachine):
+    @rule(
+        data=st.data(),
+        name=node_names,
+        array_and_chunks=np_array_and_chunks(
+            arrays=numpy_arrays(zarr_formats=st.just(3))
+        ),
+    )
+    def add_array(
+        self,
+        data: st.DataObject,
+        name: str,
+        array_and_chunks: tuple[np.ndarray[Any, Any], tuple[int, ...]],
+    ) -> None:
+        array, _ = array_and_chunks
+        # TODO: support size-0 arrays GH392
+        assume(array.size > 0)
+        # TODO: fix complex fill values GH391
+        assume(not np.iscomplexobj(array))
+        super().add_array(data, name, array_and_chunks)
+
+
+def test_zarr_hierarchy():
+    store = IcechunkStore.create(StorageConfig.memory())
+
+    def mk_test_instance_sync() -> ModifiedZarrHierarchyStateMachine:
+        return ModifiedZarrHierarchyStateMachine(store)
+
+    run_state_machine_as_test(
+        mk_test_instance_sync, settings=Settings(report_multiple_bugs=False)
+    )
+
+
+def test_zarr_store():
+    pytest.skip("icechunk is more strict about keys")
+    store = IcechunkStore.create(StorageConfig.memory())
+
+    def mk_test_instance_sync() -> ZarrHierarchyStateMachine:
+        return ZarrStoreStateMachine(store)
+
+    run_state_machine_as_test(
+        mk_test_instance_sync, settings=Settings(report_multiple_bugs=False)
+    )