var viewer = new Cesium.Viewer('cesiumContainer', {
    selectionIndicator : false,
    infoBox : false
});

var scene = viewer.scene;

var entity = viewer.entities.add({
    polygon : {
        hierarchy : Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0,
                                                        -115.0, 32.0,
                                                        -107.0, 33.0,
                                                        -102.0, 31.0,
                                                        -102.0, 35.0]),
        material : Cesium.Color.RED
    }
}); 

var handler = new Cesium.ScreenSpaceEventHandler(scene.canvas);
handler.setInputAction(function(click) {
    var pickedObject = scene.pick(click.position);
    if (Cesium.defined(pickedObject) && (pickedObject.id === entity)) {
        var positions = entity.polygon.hierarchy.getValue(viewer.clock.currentTime);
        positions[0] = Cesium.Cartesian3.fromDegrees(-110.0, 37.0);
        entity.polygon.hierarchy = positions;
    }
}, Cesium.ScreenSpaceEventType.LEFT_CLICK);