I am not 100% certain, but my guess would be around 2000-2001.

I did a search and found an article dated 9/2013 about the evolution the Pro V1. The 2000- 2001 time frame appears to be right on based on this paragraph that was in the article; "Due to the incredible momentum Pro V1 experienced in the first few months on TOUR, Titleist had to accelerate the market launch of the new ball from March 2001 to December 2000."

Another interesting paragraph that was in the article; "Back then the USGA list came out every six months, so you had to commit to a name for at least that long. There was a lot of discussion in-house and we still couldn't come up a name, so we defaulted to a lab name, which I made up -- although I thought it would only be a temporary measure. The 'Pro' comes from Professional, the 'V' is for veneer, which was the layer of Urethane, and '1' because it was the first.

http://www.pgatour.com/news/2013/09/06/the-evolution-of-the-pro-v1.html

That sounds about right.  I still have several Tour Balata 100's and just don't have the heart to get rid of them.  Best ball I've ever played.....

Those were some of the best balls EVER!  I wish they still made them

Nothing like the feel of a well struck shot with a Balata ball. Titleist balata ball's were the holy grail of golf balls.Really do miss them.That and persimmons woods.

Yep, use to put a lot of "smiley" faces on my miss hit shots, but they were good.  I still have my PB persimmon driver and occassionally swing it when I come home from work or want to just swing a little.