The Bally's/Paris chip is possible because those 2 properties hold a combined Nevada Gaming lisense. Both are owned by Park Place Entertainment (which owns many other casinos). At the time Paris was being built, it was approved by NGC to operate as an addition or annex to Bally's. This meant that it didn't have to go through the usual regulatory approvals for liscensing a new casino. However, the GCB did request a break-out financial statement from Paris, separate from Bally's.

As to other 2-property chips, Harrah's Tahoe & Reno have used some chips in common in the past. Also Nevada Lodge/Nevada Club in Tahoe & Reno (now closed). In Atlantic City, Bally's Wild Wild West casino is actually an annex of Bally's, not a different casino.

I'm sure there are others too, though not a very common practice.