Hmmm. CC did come out relatively late in the lifespan of the PSX: six months before the release of the PS2, and after the release of the Sega Dreamcast (not the most popular console, but it could have funneled some money away from PSX games for a while, especially since it was the first of its generation).
Wikipedia gives the following timeline for Japanese Squaresoft releases in late 1999:
Front Mission 3 September 2, 1999
Threads of Fate October 14, 1999
Chrono Trigger November 2, 1999 (PSX port with anime cutscenes)
Chrono Cross November 18, 1999
Parasite Eve II December 16, 1999
Chocobo Collection December 22, 1999
Enix brought out Valkyrie Profile and Torneko in roughtly the same timeframe.
There were several RPG or pseudo-RPG releases in Japan from other studios around that time, too: Legend of Dragoon, Koudelka, Growlanser I, Arc the Lad III, Dragon Valor, Fire Emblem: Thracia 776, and Shenmue. The most likely competitor is still Parasite Eve II, though.