NO, IN THE ORIGINAL EPISODE "THE SEED" CHECOV WAS NOT ON THE ENTERPRISE NOR WAS SULU
I'm going to assume this refers to the episode "Space Seed"
No, Chekov was not on the Enterprise yet. This is an early episode in the series and Chekov was not added to the show until the 2nd season. And yes, this does conflict with Chekov's recognition of the S.S. Botany Bay in Star Trek II: The Wrath of Khan.
A couple of corrections. First, Sulu was on the Enterprise during the episode "Space Seed". The first time we see Sulu, he was head of the Astrosciences department in "Where No Man Has Gone Before". Second, there is nothing in canon that prevents Chekov from being on the Enterprise during the first season, in fact, established data points seem to support it. Yes, Walter Koenig first appeared in the second season, but that does not mean that Chekov was not onboard the Enterprise already. Look at Joseph Carey on Voyager. The actor was not seen for almost six years, but Carey had to be somewhere on that ship. According to the Star Trek Chronology, Chekov was born in 2245 and attended Starfleet Academy from 2263 to 2267. Given that Kirk served on the USS Republic while still an academy cadet (Court Martial; Obsession), it seems possible that Chekov joined the Enterprise during his senior year (2266-2267) and then earned a reassignment to the bridge just before the episode "Catspaw". 188.8.131.52 03:16, May 17, 2013 (UTC)