Well, Lariat and Mibs from September 1969 both use bells, not chimes. And Skipper from October 1969 clearly uses chimes. This is easy to verify by looking at pics on IPDB that show the cabinet interior of these machines.
So I'm going to go with zacaj and IPDB on this one (post #2) that the first use of chimes in a GTB game was Skipper, October 1969. Similarly, the first use of chimes in a wedgehead (single player) was the replay game Road Race, December 1969.
The definitive answer to this question is slightly complicated by the fact that there were a couple of machines designed during these months that do not appear to be production machines. This includes the game Western (October 1969) that was apparently an Italian add-a-ball game not made in large quantities, and Auto Race, an Italian add-a-ball game that was not produced at all.
Since Western was the Italian version of Lariat, which uses bells, we can guess that Western also had bells. If anyone has a copy of this game, or has a copy of the schematic for this game, they could confirm this.
All in all, I think that it's pretty safe to say that the first production multi-player game with chimes from Gottlieb was Skipper (10/1969) and the first production wedgehead with chimes from Gottlieb was Road Race (12/1969).
Again, the source for all of the above information is from IPDB. Thank you Jay Stafford!
- TimMe