diff --git a/Lib/test/test_long.py b/Lib/test/test_long.py
index b65d24c..6788ced 100644
--- a/Lib/test/test_long.py
+++ b/Lib/test/test_long.py
@@ -202,6 +202,21 @@
                 self.assertEqual(x, y,
                     Frm("bad result for a*b: a=%r, b=%r, x=%r, y=%r", a, b, x, y))
 
+    def test_lshift_of_zero(self):
+        self.assertEqual(0L << 0, 0)
+        self.assertEqual(0L << 10, 0)
+        with self.assertRaises(ValueError):
+            0L << -1
+
+    @test_support.cpython_only
+    def test_huge_lshift_of_zero(self):
+        # Shouldn't try to allocate memory for a huge shift. See issue #27870.
+        # Other implementations may have a different boundary for overflow,
+        # or not raise at all.
+        self.assertEqual(0L << sys.maxsize, 0)
+        with self.assertRaises(OverflowError):
+            0L << (sys.maxsize + 1)
+
     def check_bitop_identities_1(self, x):
         eq = self.assertEqual
         eq(x & 0, 0, Frm("x & 0 != 0 for x=%r", x))
diff --git a/Misc/NEWS b/Misc/NEWS
index 1fd3d85..2701c7b 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -10,6 +10,9 @@
 Core and Builtins
 -----------------
 
+- Issue #27870: A left shift of zero by a large integer no longer attempts
+  to allocate large amounts of memory.
+
 - Issue #25604: Fix a minor bug in integer true division; this bug could
   potentially have caused off-by-one-ulp results on platforms with
   unreliable ldexp implementations.
diff --git a/Objects/longobject.c b/Objects/longobject.c
index 6f469bf..de2b139 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -3715,6 +3715,11 @@
         PyErr_SetString(PyExc_ValueError, "negative shift count");
         goto lshift_error;
     }
+
+    if (Py_SIZE(a) == 0) {
+        return PyLong_FromLong(0);
+    }
+
     /* wordshift, remshift = divmod(shiftby, PyLong_SHIFT) */
     wordshift = shiftby / PyLong_SHIFT;
     remshift  = shiftby - wordshift * PyLong_SHIFT;