Bruce Sutter, the Chicago Cubs and arbitrator Thomas C. Christenson did a lot of gulping and, except for Prof. Christenson after awarding the prime relief pitcher $700,000 salary for 1980, they aren't done yet.

The Cubs offered $350,000 and Sutter demanded twice that as they went before Christenson, a New York attorney, on Sunday; under major league rules, arbiter could choose only one figure or the other, no in-between.

We can imagine the Cubs saying, "Look, professor, on the basis of his work last year -- 101 innings -- he's asking for $7,000 per inning!" And we can hear the split-fingered, fast-ball expert retorting, "So? I'm only asking $16,000 per win (six) and save (37). A bargain!"

So, as Christenson put it, "You gulp twice and say, 'Okay, this is what the final result should be." And rule for the player, a record sum since the arbitration system began in 1972.

That takes care of the year left on Sutter's pact with the Cubs, so all's well that ends well, right?

Well, as Sutter headed for the Cub camp in Mesa, Ariz., yesterday, he said, "I'm very happy about the award, but it still isn't what I want. What I want is a five-year contract that will give me long-term security . . . I don't plan to pitch in spring training unless we can reopen negotiations. That doesn't mean I have to get a contract in spring training, but it does mean I'm not going to pitch until negotiations resume" . . .