diff --git a/src/tilesource.js b/src/tilesource.js
index b40598ae..84aa5a82 100644
--- a/src/tilesource.js
+++ b/src/tilesource.js
@@ -360,7 +360,8 @@ $.TileSource.prototype = {
         if (point.x >= 1) {
             x = this.getNumTiles(level).x - 1;
         }
-        if (point.y >= 1 / this.aspectRatio) {
+        var EPSILON = 1e-16;
+        if (point.y >= 1 / this.aspectRatio - EPSILON) {
             y = this.getNumTiles(level).y - 1;
         }
 
diff --git a/test/modules/tilesource.js b/test/modules/tilesource.js
index 21a9f30c..bac637c8 100644
--- a/test/modules/tilesource.js
+++ b/test/modules/tilesource.js
@@ -96,6 +96,17 @@
             maxLevel: 0,
         });
         assertTileAtPoint(0, new OpenSeadragon.Point(1, 1009 / 1006), new OpenSeadragon.Point(0, 0));
+
+        // Test for issue #1276
+        tileSource = new OpenSeadragon.TileSource({
+            width: 4036,
+            height: 1239,
+            tileWidth: 4036,
+            tileHeight: 1239,
+            tileOverlap: 0,
+            maxLevel: 0,
+        });
+        assertTileAtPoint(0, new OpenSeadragon.Point(1, 1239 / 4036), new OpenSeadragon.Point(0, 0));
     });
 
 }());