Will UN get new chief by Christmas?

The United Nations may be in for a cliffhanger of an election before it decides on a successor to the current Secretary-General, Kurt Waldheim. A decision may now have to wait until the proverbial 11th hour of Mr. Waldheim's term.

Mr. Waldheim is still expected to succeed himself. But his bid for an unprecedented third term has been thwarted so far by a consistent Chinese veto. On Tuesday the Security Council once again failed to break the current impasse.

Some diplomats here have suggested that the Chinese blocking tactic is merely a device to trap the Soviet Union.

China, according to some reports, will not lift its veto against Waldheim until the Soviet Union is obliged to veto at least one third-world candidate - presumably one from Latin America who would enter the race when and if Waldheim's challenger, Salim Salim of Tanzania, withdraws.

Thus far, the United States veto of Mr. Salim has been sufficient to shield the Soviet Union from possibly casting its veto against Mr. Salim, who is presumed to be too pro-Chinese for Moscow.

The Soviet Union is widely believed to favor the continuation of the present impasse in the hope that come Christmas, with only a few days left before the expiration of Mr. Waldheim's mandate, the pressure on China to lift its veto will become irresistible.

Thus Waldheim would be reappointed without the Soviet Union having to cast an anti-third-world veto. China has vetoed Mr. Waldheim to show its third-world sympathies.

As a result, the problem remains as it has for these past few weeks and after a succession of inconclusive ballots: Mr. Waldheim, the leading candidate, cannot, as yet, escape a recurring Chinese veto.

His challenger, Tanzanian Ambassador Salim Salim, cannot overcome a United States veto. He refuses to bow out of the race, even though he does not poll as well among the 15 participating Security Council members as Waldheim.

Two stumbling blocks essentially have brought the Security Council to a standstill:

1. Soviet-Chinese rivalry in courting the third world, an exercise that one Council member calls a ''competition in demagoguery'' since both would like ''to eat their cake and have it,'' that is, reappoint Waldheim and still appear to be pro-third-worldish.

2. The stridency and determination of a small group of third-world radicals who tie Salim's cause to that of Africa and try to make a personal issue into a political, albeit an ethnic, one.

Meanwhile the work of the General Assembly, which must ultimately approve the choice of the Security Council, is virtually paralyzed by the prevailing mood of suspense engendered by the the Council deadlock.

A growing number of delegations are concerned that the institution itself could be tarnished and that the authority of the next secretary-general will be diminished.

In the end, the odds remain strongly in favor of Kurt Waldheim's reappointment, since he is the only candidate acceptable to the two superpowers as well as to the vast majority of third-world countries.