Who really was first to the North Pole?

''The unknown belongs to whomever gets there first,'' said explorer Frederick A. Cook. The problem, according to Cook and Peary: The Race to the Pole (CBS, Tuesday, Dec. 13, 9-11 p.m.), is determining exactly who did get there first.

This complex ITT Theatre Special concerns man's pride of achievement, two men's private and public ambitions, and the hypocrisy which sometimes conceals certain men's real motivations.

As fascinatingly detailed in a tight script by I.C. Rapoport, sparingly directed by Robert Day, and impeccably acted by Richard Chamberlain as Cook and Rod Steiger as Robert E. Peary, ''The Race to the Pole'' definitely sides with Cook in the still-continuing controversy as to which one of the men actually reached ''the big nail'' - the North Pole.

In what amounts to a series of gorgeously photographed tableaux, the drama traces the difficulties of Arctic expeditions and the frightening struggle for survival, then the political maneuvering which often follows successful explorations.

The seemingly dishonest Peary emerged on top in his own time and was hailed as a hero while Cook lived out his life dishonored and discredited. Only now are some giving him credit for what seems to be his very real triumph.

''Cook and Peary: The Race to the Pole'' takes a long, cold, very cold, look at the harm which overcompetitiveness can do to men's values and judgments. Perhaps there are truly Olympian lessons to be learned.