Chip antenna, what to do with power and bottom planes
You should maintain the prescribed keepout zone on all layers1.  You will need a ground copper pour for the matching network on the top layer near the antenna.  It should be "stitched" with vias to the inner layer ground plane.  

My gut feeling tells me that it's not a bad idea to have ground on every layer around the keepout zone.  I would make a via "fence" around the keepout zone.

1 What ThePhoton said in his comment.

2 Molex app note for this antenna.

3 I'm not an RF and antenna expert.  An actual RF speciallist can do this question better justice. I'm writing this answer only as a fallback.