diff --git a/news/+traced-constant-sum.bugfix.rst b/news/+traced-constant-sum.bugfix.rst
new file mode 100644
index 00000000..e2b1b2f9
--- /dev/null
+++ b/news/+traced-constant-sum.bugfix.rst
@@ -0,0 +1,3 @@
+Allow a traced scalar constant on the left of a kernel sum when using JIT,
+automatic differentiation, or vectorization. Keep the builtin-zero shortcut
+used by Python's ``sum``.
diff --git a/src/tinygp/kernels/base.py b/src/tinygp/kernels/base.py
index 8df5077b..0bfa6dfd 100644
--- a/src/tinygp/kernels/base.py
+++ b/src/tinygp/kernels/base.py
@@ -109,7 +109,7 @@ def __add__(self, other: Kernel | JAXArray) -> Kernel:
 
     def __radd__(self, other: Any) -> Kernel:
         # We'll hit this first branch when using the `sum` function
-        if other == 0:
+        if isinstance(other, (int, float)) and other == 0:
             return self
         if isinstance(other, Kernel):
             return Sum(other, self)
diff --git a/tests/test_kernels/test_traced_constant_sum.py b/tests/test_kernels/test_traced_constant_sum.py
new file mode 100644
index 00000000..6f45f14c
--- /dev/null
+++ b/tests/test_kernels/test_traced_constant_sum.py
@@ -0,0 +1,49 @@
+import jax
+import jax.numpy as jnp
+import pytest
+
+from tinygp import GaussianProcess, kernels
+from tinygp.test_utils import assert_allclose
+
+
+@pytest.mark.parametrize("constant", [0.0, 0.5])
+def test_left_constant_sum_under_jax_transforms(constant):
+    x = jnp.linspace(-1, 1, 5)
+    kernel = kernels.ExpSquared(0.7)
+
+    def evaluate(value):
+        return (value + kernel)(x, x)
+
+    assert_allclose(jax.jit(evaluate)(constant), kernel(x, x) + constant)
+    derivative = jax.jit(jax.jacrev(evaluate))(constant)
+    assert_allclose(derivative, jnp.ones((len(x), len(x))))
+    constants = jnp.array([0.0, 0.5, 1.0])
+    expected = kernel(x, x)[None] + constants[:, None, None]
+    assert_allclose(jax.vmap(evaluate)(constants), expected)
+
+
+def test_left_constant_sum_gp_likelihood_gradient():
+    x = jnp.linspace(-1, 1, 5)
+    y = jnp.sin(x)
+    kernel = kernels.ExpSquared(0.7)
+
+    def left(value):
+        return GaussianProcess(value + kernel, x, diag=0.1).log_probability(y)
+
+    def dense_reference(value):
+        covariance = kernel(x, x) + value + 0.1 * jnp.eye(len(x))
+        return jax.scipy.stats.multivariate_normal.logpdf(
+            y, jnp.zeros_like(y), covariance
+        )
+
+    actual = jax.jit(jax.value_and_grad(left))(0.5)
+    expected = jax.jit(jax.value_and_grad(dense_reference))(0.5)
+    assert_allclose(actual[0], expected[0])
+    assert_allclose(actual[1], expected[1])
+
+
+def test_builtin_zero_sum_keeps_kernel_identity():
+    kernel = kernels.ExpSquared(0.7)
+    assert 0 + kernel is kernel
+    assert 0.0 + kernel is kernel
+    assert sum([kernel]) is kernel