diff --git a/tests/test_properties.py b/tests/test_properties.py
new file mode 100644
index 0000000000..b3152ea0e3
--- /dev/null
+++ b/tests/test_properties.py
@@ -0,0 +1,109 @@
+import pytest
+
+pytest.importorskip("hypothesis")
+
+import zarr
+import numpy as np
+
+from hypothesis import settings
+import hypothesis.strategies as st
+import hypothesis.extra.numpy as npst
+from hypothesis import given, settings
+from zarr.core import Array
+
+from zarr._storage.v3 import KVStoreV3
+from zarr.storage import init_array, normalize_store_arg
+
+#### TODO: Provide this in zarr.strategies
+# Copied from Xarray
+# only use characters within the "Latin Extended-A" subset of unicode
+_readable_characters = st.characters(categories=["L", "N"], max_codepoint=0x017F)
+_readable_strings = st.text(_readable_characters, max_size=5)
+_attr_keys = st.text(_readable_characters, min_size=1)
+_attr_values = st.recursive(
+    st.none() | st.booleans() | _readable_strings,
+    lambda children: st.lists(children) | st.dictionaries(_attr_keys, children),
+    max_leaves=3,
+)
+
+# No '/' in array names?
+# No '.' in paths?
+zarr_key_chars = st.sampled_from("-0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ_abcdefghijklmnopqrstuvwxyz")
+
+# The following should be public strategies
+attrs = st.none() | st.dictionaries(_attr_keys, _attr_values)
+paths = st.none() | st.text(zarr_key_chars, min_size=1) | st.just("/")
+array_names = st.text(zarr_key_chars | st.just("."), min_size=1).filter(
+    lambda t: not t.startswith((".", ".."))
+)
+
+
+@st.composite
+def array_strategy(draw):
+    """A hypothesis strategy to generate small sized random arrays.
+
+    Returns: a tuple of the array and a suitable random chunking for it.
+    """
+    array = draw(npst.arrays(dtype=npst.scalar_dtypes(), shape=npst.array_shapes(max_dims=4)))
+    # We want this strategy to shrink towards arrays with smaller number of chunks
+    # 1. st.integers() shrinks towards smaller values. So we use that to generate number of chunks
+    numchunks = draw(st.tuples(*[st.integers(min_value=1, max_value=size) for size in array.shape]))
+    # 2. and now generate the chunks tuple
+    chunks = tuple(size // nchunks for size, nchunks in zip(array.shape, numchunks))
+    return (array, chunks)
+
+
+#####
+
+
+# @pytest.mark.slow
+@settings(max_examples=300)
+@given(path=paths, attrs=attrs, name=array_names, array_and_chunks=array_strategy())
+def test_roundtrip(path, array_and_chunks, name, attrs):
+    store = KVStoreV3(dict())
+
+    nparray, chunks = array_and_chunks
+
+    # TODO: clean this up
+    if path is None and name is None:
+        array_path = None
+        array_name = None
+    elif path is None and name is not None:
+        array_path = f"{name}"
+        array_name = f"/{name}"
+    elif path is not None and name is None:
+        array_path = path
+        array_name = None
+    elif path == "/":
+        assert name is not None
+        array_path = name
+        array_name = "/" + name
+    else:
+        assert name is not None
+        array_path = f"{path}/{name}"
+        array_name = "/" + array_path
+
+    expected_attrs = {} if attrs is None else attrs
+
+    init_array(store, shape=nparray.shape, chunks=chunks, path=array_path, dtype=nparray.dtype.str)
+    a = Array(store, path=array_path, zarr_version=3)
+    if attrs is not None:
+        a.attrs.put(attrs)
+
+    assert isinstance(a, Array)
+    assert nparray.shape == a.shape
+    assert chunks == a.chunks
+    assert array_path == a.path
+    assert array_name == a.name
+    # assert a.basename is None  # TODO
+    assert a.store == normalize_store_arg(store)
+    assert a.attrs.asdict() == expected_attrs
+
+    a[:] = nparray
+
+    store.close()
+
+    group = zarr.open_group(store)
+    actual = group[array_path]
+    assert actual.attrs.asdict() == expected_attrs
+    np.testing.assert_equal(nparray, np.array(actual))