diff --git a/Lib/test/test_traceback.py b/Lib/test/test_traceback.py
index f9a5f2fc53e1e9..5b362cfc7d3e8c 100644
--- a/Lib/test/test_traceback.py
+++ b/Lib/test/test_traceback.py
@@ -632,6 +632,54 @@ def outer_raise():
         self.check_zero_div(blocks[0])
         self.assertIn('inner_raise() # Marker', blocks[2])
 
+    def test_rho_context(self):
+        # Make sure that rho-shaped linked lists of __context__s do
+        # not get stuck in an infinite loop. See bpo-40696.
+        with self.assertRaises(ValueError) as cm:
+            # ValueError -> RuntimeError ↺
+            try:
+                raise RuntimeError #rho1
+            except Exception as exc:
+                x = exc
+                x.__context__ = x
+                raise ValueError #rho1
+
+        blocks = boundaries.split(self.get_report(cm.exception))
+        self.assertEqual(len(blocks), 3, blocks)
+        self.assertIn('RuntimeError #rho1', blocks[0])
+        self.assertEqual(blocks[1], context_message)
+        self.assertIn('ValueError', blocks[2])
+
+    def test_rho_context_2(self):
+        with self.assertRaises(ValueError) as cm:
+            # ValueError -> IndexError -> SyntaxError <=> ZeroDivisionError
+            try:
+                raise ZeroDivisionError #rho2
+            except Exception as exc:
+                y = exc
+
+            try:
+                raise SyntaxError #rho2
+            except Exception as exc:
+                z = exc
+                z.__context__ = y
+                y.__context__ = z
+                try:
+                    raise IndexError #rho2
+                except IndexError:
+                    raise ValueError #rho2
+
+        blocks = boundaries.split(self.get_report(cm.exception))
+        self.assertEqual(len(blocks), 7)
+        self.assertIn('ZeroDivisionError #rho2', blocks[0])
+        self.assertEqual(blocks[1], context_message)
+        self.assertIn('SyntaxError #rho2', blocks[2])
+        self.assertEqual(blocks[3], context_message)
+        self.assertIn('IndexError #rho2', blocks[4])
+        self.assertEqual(blocks[5], context_message)
+        self.assertIn('ValueError', blocks[6])
+
+
     def test_cause_recursive(self):
         def inner_raise():
             try:
diff --git a/Misc/NEWS.d/next/Core and Builtins/2020-05-30-12-13-35.bpo-40696.NJZ364.rst b/Misc/NEWS.d/next/Core and Builtins/2020-05-30-12-13-35.bpo-40696.NJZ364.rst
new file mode 100644
index 00000000000000..cc9af5b45354cb
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2020-05-30-12-13-35.bpo-40696.NJZ364.rst	
@@ -0,0 +1 @@
+The interpreter no longer hangs when it encounters exceptions whose ``__context__`` attributes formed a cycle. Patch by Dennis Sweeney.
diff --git a/Python/errors.c b/Python/errors.c
index 70365aaca585bb..c2911832fee103 100644
--- a/Python/errors.c
+++ b/Python/errors.c
@@ -98,6 +98,16 @@ _PyErr_CreateException(PyObject *exception, PyObject *value)
     }
 }
 
+static inline PyObject *
+GET_CONTEXT(PyObject *exc)
+{
+    if (exc == NULL) {
+        return NULL;
+    }
+    assert(PyExceptionInstance_Check(exc));
+    return ((PyBaseExceptionObject *)exc)->context;
+}
+
 void
 _PyErr_SetObject(PyThreadState *tstate, PyObject *exception, PyObject *value)
 {
@@ -136,25 +146,49 @@ _PyErr_SetObject(PyThreadState *tstate, PyObject *exception, PyObject *value)
             value = fixed_value;
         }
 
-        /* Avoid reference cycles through the context chain.
-           This is O(chain length) but context chains are
-           usually very short. Sensitive readers may try
-           to inline the call to PyException_GetContext. */
-        if (exc_value != value) {
-            PyObject *o = exc_value, *context;
-            while ((context = PyException_GetContext(o))) {
-                Py_DECREF(context);
-                if (context == value) {
-                    PyException_SetContext(o, NULL);
-                    break;
-                }
-                o = context;
-            }
-            PyException_SetContext(value, exc_value);
+        if (value == exc_value) {
+            /* This exception is already on top of the stack. */
+            Py_DECREF(exc_value);
         }
         else {
-            Py_DECREF(exc_value);
+            /* Otherwise, push the new value on top. */
+            PyException_SetContext(value, exc_value);
+
+            /* Now we need to destroy any reference cycles that might
+               exist in the chain of contexts. Use Floyd's cycle-finding
+               algorithm to determine if the chain has a cycle or if it
+               reaches NULL. */
+            PyObject *tortoise = GET_CONTEXT(value);
+            PyObject *hare = GET_CONTEXT(GET_CONTEXT(value));
+            while (hare != NULL && hare != tortoise) {
+                tortoise = GET_CONTEXT(tortoise);
+                hare = GET_CONTEXT(GET_CONTEXT(hare));
+            }
+            if (hare != NULL) {
+                /* Making it here means there is a cycle.
+                   Now find the _first_ self-intersection. */
+                tortoise = value;
+                while (tortoise != hare) {
+                    tortoise = GET_CONTEXT(tortoise);
+                    hare = GET_CONTEXT(hare);
+                }
+                /* Now hare is the first intersection.
+                   We want to disconnect hare from its second predecessor.
+                   For example:
+                   A --> B --> C --> D --> E --> C --> ...
+                   becomes
+                   A --> B --> C --> D --> E --> NULL,
+                   since C is the first intersection.
+                   */
+                PyObject *prev = hare, *next = GET_CONTEXT(hare);
+                while (next != hare) {
+                    prev = next;
+                    next = GET_CONTEXT(next);
+                }
+                PyException_SetContext(prev, NULL);
+            }
         }
+
     }
     if (value != NULL && PyExceptionInstance_Check(value))
         tb = PyException_GetTraceback(value);