diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2026-11-03-13-44-26.gh-issue-159184.X_sOdY.rst b/Misc/NEWS.d/next/Core_and_Builtins/2026-11-03-13-44-26.gh-issue-159184.X_sOdY.rst
new file mode 100644
index 00000000000000..651ac1d0b9bae9
--- /dev/null
+++ b/Misc/NEWS.d/next/Core_and_Builtins/2026-11-03-13-44-26.gh-issue-159184.X_sOdY.rst
@@ -0,0 +1,2 @@
+Fix a leak of NaN constants in code objects created by :func:`marshal.loads`
+on the free-threaded build.
diff --git a/Objects/codeobject.c b/Objects/codeobject.c
index eb390ab24ec13e..2255220bec3d30 100644
--- a/Objects/codeobject.c
+++ b/Objects/codeobject.c
@@ -173,8 +173,16 @@ should_immortalize_constant(PyObject *v)
                 _Py_IsImmortal(slice->stop) &&
                 _Py_IsImmortal(slice->step));
     }
-    return (PyLong_CheckExact(v) || PyFloat_CheckExact(v) ||
-            PyComplex_CheckExact(v) || PyBytes_CheckExact(v));
+    // The hash of a NaN depends on its address, so the table would keep every
+    // NaN object it gets (and merging them would shrink frozensets).
+    if (PyFloat_CheckExact(v)) {
+        return !isnan(PyFloat_AS_DOUBLE(v));
+    }
+    if (PyComplex_CheckExact(v)) {
+        Py_complex c = ((PyComplexObject *)v)->cval;
+        return !isnan(c.real) && !isnan(c.imag);
+    }
+    return PyLong_CheckExact(v) || PyBytes_CheckExact(v);
 }
 #endif