diff --git a/Include/internal/pycore_ceval.h b/Include/internal/pycore_ceval.h
index b9f2d7d1758537..f087879d0c103c 100644
--- a/Include/internal/pycore_ceval.h
+++ b/Include/internal/pycore_ceval.h
@@ -11,6 +11,19 @@ extern "C" {
 #include "pycore_atomic.h"
 #include "pythread.h"
 
+struct _pending_call;
+
+struct _pending_call {
+    int (*func)(void *);
+    void *arg;
+    struct _pending_call *next;
+};
+
+// We technically do not need this limit around any longer since we
+// moved from a circular queue to a linked list.  However, having a
+// size limit is still a good idea so we keep the one we already had.
+#define NPENDINGCALLS 32
+
 struct _pending_calls {
     unsigned long main_thread;
     PyThread_type_lock lock;
@@ -20,13 +33,9 @@ struct _pending_calls {
        thread state.
        Guarded by the GIL. */
     int async_exc;
-#define NPENDINGCALLS 32
-    struct {
-        int (*func)(void *);
-        void *arg;
-    } calls[NPENDINGCALLS];
-    int first;
-    int last;
+    int ncalls;
+    struct _pending_call *head;
+    struct _pending_call *last;
 };
 
 #include "pycore_gil.h"
diff --git a/Misc/NEWS.d/next/Core and Builtins/2018-12-11-15-12-03.bpo-35466.5xu737.rst b/Misc/NEWS.d/next/Core and Builtins/2018-12-11-15-12-03.bpo-35466.5xu737.rst
new file mode 100644
index 00000000000000..43ae1bf3ce1344
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2018-12-11-15-12-03.bpo-35466.5xu737.rst	
@@ -0,0 +1 @@
+Simply the ceval pending calls list by using a linked list.
diff --git a/Python/ceval.c b/Python/ceval.c
index 3e82ceb952510e..8654915752b0e9 100644
--- a/Python/ceval.c
+++ b/Python/ceval.c
@@ -322,6 +322,48 @@ _PyEval_SignalReceived(void)
     SIGNAL_PENDING_SIGNALS();
 }
 
+static int
+_add_pending_call(int (*func)(void *), void *arg)
+{
+    // TODO: Drop the limit?
+    if (_PyRuntime.ceval.pending.ncalls == NPENDINGCALLS) {
+        return -1; /* Queue full */
+    }
+
+    struct _pending_call *call = PyMem_RawMalloc(sizeof(struct _pending_call));
+    if (call == NULL) {
+        return -1;
+    }
+    call->func = func;
+    call->arg = arg;
+    call->next = NULL;
+
+    if (_PyRuntime.ceval.pending.head == NULL) {
+        _PyRuntime.ceval.pending.head = call;
+    }
+    else {
+        _PyRuntime.ceval.pending.last->next = call;
+    }
+    _PyRuntime.ceval.pending.last = call;
+    _PyRuntime.ceval.pending.ncalls++;
+    return 0;
+}
+
+static void
+_pop_pending_call(int (**func)(void *), void **arg)
+{
+    struct _pending_call *call = _PyRuntime.ceval.pending.head;
+    if (call == NULL) {
+        return; /* Queue empty */
+    }
+    _PyRuntime.ceval.pending.head = call->next;
+    _PyRuntime.ceval.pending.ncalls--;
+
+    *func = call->func;
+    *arg = call->arg;
+    PyMem_RawFree(call);
+}
+
 /* This implementation is thread-safe.  It allows
    scheduling to be made from any thread, and even from an executing
    callback.
@@ -330,7 +372,6 @@ _PyEval_SignalReceived(void)
 int
 Py_AddPendingCall(int (*func)(void *), void *arg)
 {
-    int i, j, result=0;
     PyThread_type_lock lock = _PyRuntime.ceval.pending.lock;
 
     /* try a few times for the lock.  Since this mechanism is used
@@ -345,6 +386,7 @@ Py_AddPendingCall(int (*func)(void *), void *arg)
      * this function is called before any bytecode evaluation takes place.
      */
     if (lock != NULL) {
+        int i;
         for (i = 0; i<100; i++) {
             if (PyThread_acquire_lock(lock, NOWAIT_LOCK))
                 break;
@@ -353,20 +395,13 @@ Py_AddPendingCall(int (*func)(void *), void *arg)
             return -1;
     }
 
-    i = _PyRuntime.ceval.pending.last;
-    j = (i + 1) % NPENDINGCALLS;
-    if (j == _PyRuntime.ceval.pending.first) {
-        result = -1; /* Queue full */
-    } else {
-        _PyRuntime.ceval.pending.calls[i].func = func;
-        _PyRuntime.ceval.pending.calls[i].arg = arg;
-        _PyRuntime.ceval.pending.last = j;
-    }
+    int res = _add_pending_call(func, arg);
+
     /* signal main loop */
     SIGNAL_PENDING_CALLS();
     if (lock != NULL)
         PyThread_release_lock(lock);
-    return result;
+    return res;
 }
 
 static int
@@ -420,24 +455,18 @@ make_pending_calls(void)
 
     /* perform a bounded number of calls, in case of recursion */
     for (int i=0; i<NPENDINGCALLS; i++) {
-        int j;
-        int (*func)(void *);
+        int (*func)(void *) = NULL;
         void *arg = NULL;
 
         /* pop one item off the queue while holding the lock */
         PyThread_acquire_lock(_PyRuntime.ceval.pending.lock, WAIT_LOCK);
-        j = _PyRuntime.ceval.pending.first;
-        if (j == _PyRuntime.ceval.pending.last) {
-            func = NULL; /* Queue empty */
-        } else {
-            func = _PyRuntime.ceval.pending.calls[j].func;
-            arg = _PyRuntime.ceval.pending.calls[j].arg;
-            _PyRuntime.ceval.pending.first = (j + 1) % NPENDINGCALLS;
-        }
+        _pop_pending_call(&func, &arg);
         PyThread_release_lock(_PyRuntime.ceval.pending.lock);
+
         /* having released the lock, perform the callback */
-        if (func == NULL)
+        if (func == NULL) {
             break;
+        }
         res = func(arg);
         if (res) {
             goto error;