Like hundreds of other American chess players, Mr. Cherniack and a host of other young men at the tournament date their obsession with chess to the summer of 1972, when Bobby Fischer overwhelmed Mr. Spassky, then world champion, in Iceland to win the world title and become an American hero. Mr. Fischer has not played a single game of chess in public since. He forfeited his world title in 1975. 'I'm Already Somewhat Famous'

The legend of Bobby Fischer hangs over the New York Open. The younger chess players, who dream of their game's one day attaining a status among the public equal to such pas times as baseball or tennis, with all the accompanying financial rewards, talked in bitter tones of Mr. Fischer as their great lost hope.

''If Bobby Fischer had stayed in chess, a lot more people would be interested in it,'' said Joel Benjamin, 23, who is the fourth-best chess player in the United States and Number 32 in the world. ''I'm already somewhat famous in the chess world. I'd like to see the day when chess players are known among the public like athletes.''

Mr. Benjamin pointed out that while he might be treated with all due respect among the crowd at the Penta Hotel, he nevertheless had no hope of getting a last-minute ticket to Thursday night's Rangers game at Madison Square Garden.

In hopes of one day becoming a world champion, Mr. Benjamin, a Yale graduate from the Marine Park section of Brooklyn, said he will be moving to Barcelona next month to pursue chess under the tutelage of John Fedorowicz, a grandmaster from New York. 'I Go Home at Night'

At age 44, Asa Hoffmann, a onetime New York City junior champion and vice president of the Manhattan Chess Club, no longer dreams of becoming champion of the world. ''When you first start playing, the game is so great that it's easy to just hang out and play day and night,'' he said. ''But I've become domesticated. Now, I go home at night to my woman and watch old movies on TV''

Still, he is a celebrity in his own right at the New York Open, which is organized by Jose Cuchi, a New York City jewelry manufacturer and chess fanatic. He is playing respectably in the regular master's division. He is a superstar in the low-stakes, high-speed blitz chess games played, unofficially, in the hotel's Dartmouth Room. He said he can pick up a few hundred dollars at blitz chess during the tournament, at $3 to $5 a game.