Professional Chess Association
The Professional Chess Association (PCA), which existed between 1993 and 1996, was a rival organisation to FIDE, the international chess organization. The PCA was created in 1993 by Garry Kasparov and Nigel Short for the marketing and organization of their chess world championship.
By FIDE regulation, the bids for the World Championship final should have been decided by three parties - FIDE, the World Champion (Kasparov) and the Challenger (Short). According to Kasparov and Short, FIDE president Florencio Campomanes broke these rules by simply announcing the venue of winning bid as being Manchester. FIDE derived a substantial part of its income from the prize fund of the World Championship.
In response to this, Kasparov and Short formed the PCA, appointing Bob Rice as Commissioner. They played their world championship match under its auspices in October 1993. The match took place in the Savoy Theatre in London, under the sponsorship of The Times. Kasparov won clearly 12.5-7.5 and became PCA World Chess Champion.
FIDE stripped Kasparov of the FIDE World Championship title, and instead held a rival match between Anatoly Karpov and Jan Timman, the two final players Short had defeated to win the Candidates Tournament. Karpov won that match, to become FIDE World Chess Champion. For the first time in chess history there were two world champions, the FIDE world champion Karpov and the PCA world champion Kasparov.
1995 cycle 
From 1993 to 1995, the PCA held an Interzonal tournament and Candidates matches, in the style of the FIDE world championship qualifiers. FIDE also had its own cycle of qualifiers, with many of the same players playing in both. The PCA candidates cycle was won by the Indian GM Viswanathan Anand.
Demise and aftermath 
The PCA lost its main sponsor, Intel, in 1996, as retaliation for Kasparov's choice to play a match against IBM's supercomputer Deep Blue earlier that year, which boosted the fame of IBM, a main rival of Intel's; the PCA folded soon afterwards. This left Kasparov unable to organise a proper qualifying cycle for his title. He finally played (and lost) a match to a hand picked challenger, Vladimir Kramnik, in 2000 (Classical World Chess Championship 2000). This match was played under the auspices of Braingames.
When Kramnik defended his title at the Classical World Chess Championship 2004, he gave the title the name "Classical", to emphasise the continuity that his title had with the tradition of defeating the previous titleholder. Since this is the same title as the Kasparov's PCA World title, the PCA World title is sometimes retrospectively called the "Classical" title.