Kind of hard to tell from the scan but yours does not look like a DiaSq.
It looks like a SqSqDia, if so it is probably lost to history.
Your chip would have been made at the Burt Co in Maine. Caro and Fils in Chicago would have put the hot stamp on. I know of no records from Caro.

Your only hope is to find the person that either sold or bought the chip. If I was going to take this one on, I would call everyone in the Chicago phone book with the last name of either Caro or Fils. There is a good chance you will find a relative of one of the owners, maybe one of the owners, maybe the records on the company. This system has worked for me in the past but sometimes it is fruitless.

I once called everyone in the US with the last name of Kriter, and got zip.
On another occiasion I was researching a chip with the name O'Shea associated with it. I got his daughter on the 1st call and all my questions were answered.

IMO, your chip is either a promotional chip or possibly a home game chip.