OK, this might be a long shot. But if you Google, Andy's San Jose, one of the many thing that comes up is Andy's Pet Shop, which was opened in 1950 near downtown San Jose by Andy and his wife Geraldine Camilleri, according to the pet shop website. They put up this neon sign sometimes afterwards. The slanted font it very similar to that on the chip, and both even have the same small triangular notch out of the top left of the A. The apostrophe however is placed in a slightly different place. Their daughters ran the business until they sold it in 1993.

I know it was common to gamble in the back of cigar and even candy stores during this era, so maybe in a back room of a pet store? I can imagine the stories.