--- a/widget/SystemTimeConverter.h
+++ b/widget/SystemTimeConverter.h
@@ -44,22 +44,27 @@ public:
   {
     static_assert(!IsSigned<Time>::value, "Expected Time to be unsigned");
   }
 
   template <typename CurrentTimeGetter>
   mozilla::TimeStamp
   GetTimeStampFromSystemTime(Time aTime,
                              CurrentTimeGetter& aCurrentTimeGetter) {
+    TimeStamp roughlyNow = TimeStamp::Now();
+
     // If the reference time is not set, use the current time value to fill
     // it in.
     if (mReferenceTimeStamp.IsNull()) {
+      // This sometimes happens when ::GetMessageTime returns 0 for the first
+      // message on Windows.
+      if (!aTime)
+        return roughlyNow;
       UpdateReferenceTime(aTime, aCurrentTimeGetter);
     }
-    TimeStamp roughlyNow = TimeStamp::Now();
 
     // Check for skew between the source of Time values and TimeStamp values.
     // We do this by comparing two durations (both in ms):
     //
     // i.  The duration from the reference time to the passed-in time.
     //     (timeDelta in the diagram below)
     // ii. The duration from the reference timestamp to the current time
     //     based on TimeStamp::Now.