diff --git a/cubed/__init__.py b/cubed/__init__.py
index 9134619d0..a87e912fb 100644
--- a/cubed/__init__.py
+++ b/cubed/__init__.py
@@ -337,6 +337,6 @@
 
 # extensions
 
-from .array_api import linalg
+from .array_api import fft, linalg
 
-__all__ += ["linalg"]
+__all__ += ["fft", "linalg"]
diff --git a/cubed/array_api/fft.py b/cubed/array_api/fft.py
new file mode 100644
index 000000000..d690e4221
--- /dev/null
+++ b/cubed/array_api/fft.py
@@ -0,0 +1,39 @@
+from cubed.backend_array_api import namespace as nxp
+from cubed.core.ops import map_blocks
+
+
+def fft(x, /, *, n=None, axis=-1, norm="backward"):
+    return fft_1d(nxp.fft.fft, x, n=n, axis=axis, norm=norm)
+
+
+def ifft(x, /, *, n=None, axis=-1, norm="backward"):
+    return fft_1d(nxp.fft.ifft, x, n=n, axis=axis, norm=norm)
+
+
+def fft_1d(fft_func, x, /, *, n=None, axis=-1, norm="backward"):
+    if x.numblocks[axis] > 1:
+        raise ValueError(
+            "FFT can only be applied along axes with a single chunk. "
+            # TODO: give details about what was tried and mention rechunking (see qr message)
+        )
+
+    if n is None:
+        chunks = x.chunks
+    else:
+        chunks = list(x.chunks)
+        chunks[axis] = (n,)
+
+    return map_blocks(
+        _fft,
+        x,
+        dtype=nxp.complex128,
+        chunks=chunks,
+        fft_func=fft_func,
+        n=n,
+        axis=axis,
+        norm=norm,
+    )
+
+
+def _fft(a, fft_func=None, n=None, axis=None, norm=None):
+    return fft_func(a, n=n, axis=axis, norm=norm)
diff --git a/cubed/tests/test_fft.py b/cubed/tests/test_fft.py
new file mode 100644
index 000000000..3b408538d
--- /dev/null
+++ b/cubed/tests/test_fft.py
@@ -0,0 +1,28 @@
+import pytest
+from numpy.testing import assert_allclose
+
+import cubed
+import cubed.array_api as xp
+from cubed.backend_array_api import namespace as nxp
+
+
+@pytest.mark.parametrize("funcname", ["fft", "ifft"])
+@pytest.mark.parametrize("n", [None, 5, 13])
+def test_fft(funcname, n):
+    nxp_fft = getattr(nxp.fft, funcname)
+    cb_fft = getattr(xp.fft, funcname)
+
+    an = nxp.arange(100).reshape(10, 10)
+    bn = nxp_fft(an, n=n)
+    a = cubed.from_array(an, chunks=(1, 10))
+    b = cb_fft(a, n=n)
+
+    assert_allclose(b.compute(), bn)
+
+
+def test_fft_chunked_axis_fails():
+    an = nxp.arange(100).reshape(10, 10)
+    a = cubed.from_array(an, chunks=(1, 10))
+
+    with pytest.raises(ValueError):
+        xp.fft.fft(a, axis=0)