Personally I wonder on which of these chips development began first, and which one was soonest finished:
POKEY - Assumed development started in the summer of 1977, finished in 9 months (spring 1978) and demoed in the Atari 400/800 in January 1979. It also strikes me that development of the next generation gaming hardware was initiated before the VCS had been launched to customers, but perhaps constant development is a given.
AY-3-891x - Apparently GI had the AY-3-8900 STIC ready by January 1978, but not sure about the 891x sound chip. The Intellivision though is said to have been developed during 1978 and test marketed in late 1979 in California.
TMS9919 - It was pre-dated by the short lived SN76477 which only featured one channel of sound that could be either a sine wave, a square wave or noise, although with envelope control. This chip was found in Space Invaders from June 1978, but was soon replaced with the SN76489/TMS9919 with better capacities to match the already popular (?) AY-3-8910. Another time marker is the ALF Music Card MC16 for the Apple ][ that was demonstrated in late 1978 and for sale in early 1979. It is said that the 9919 pretty much is a single chip version of the MC16. Finally the TI-99/4 was demoed in June 1979, so by then the sound chip for sure must've been ready.
For further dating, there is a resource on the TMS9918 VDP that is rather vague about dating, but it mentions the hardware sprites were inspired by Atari, which I assume would put development no sooner than September 1977, unless TI engineers got a sneak peak. There is a timing document on the VDP from 1978, which matches the dating for the companion sound chip.
Thus, it is a good possibility all three of those sound chips were worked on simultaneously. Perhaps GI actually predated Atari a little on this, which would suggest this order of chips being ready:
(three years later)
It's not surprising to hear the AY chip may have come first.
General Instruments produced a series of pong and other game chips between 1976 and 1978.