You have access to the inside of the machine, right? If not, you're out of luck.

Open the main cabinet, and look for a weight suspended on a metal rod. Sort of cone-shaped, with the wider part facing down. I can't say where it will be in Slick Chick (that's from back in 1963 I think), but usually it will be located on the left side of the cabinet, towards the front of the machine. The weight can be moved up or down (look for a wing nut or other adjustment beneath it). When the weight touches the metal ring around it -- boom -- TILT.

If that doesn't fix the problem, it might be another switch that's to blame. There is probably at least one (and maybe two or three) "slam tilt" switches on the machine also. Those are there to protect it from extreme abuse, such as slamming the machine with your fist (hence the name). Look on the coin door, that's where you'll usually find at least one of these. On old Gottliebs, I *think* that these switches are supposed to be normally closed, but I could be wrong about that.

There are MANY pinball resources on the Internet if you need more help. I've listed two places for you to start...