"Choreography by Balanchine," which opens a third season for public TV's splendid "Dance in America" series tonight, is quite possibly television's finest achievement to date with respect to the terspichorean arts. The reason is easy to pin down - a winning combination of first-class dance material and video direction sensitive to its special needs.

Tonight's hour-long program (on Channel 26 at 9 o'clock) is actually the fisrt of two devoted to the work of George Balanchine and the New York City Ballet. The company he co-directs with Lincoln Kristein. The fare includes "Tzigane," from the company's 1975 Ravel festival; the Andante from "Divertimento No. 15" (Mozart), dating from 1956: and "Four Temperaments," to a Hindemith score, from 1946.

One week from tonight, a second, 90 minute program will offer excerpts from the 1967 colossus, "Jewels," and the "Stravinsky Violin Concerto" composed in 1972 for the company's Stravinsky festival.

No sampling of six works could be called "representative" of the output of a man who has created 200 very diversified ballets, but this is a good, strong assortment more than sufficient to show why Balanchine is universally regarded the master choreographer of our era.

And the "Dance in America" production team, led by director Merrill Brockway, has outstripped its own fine record in the care and intelligence of the visual treatment. Cutting is kept to a minimum. Shooting angles are cannily chosen to enhance both the lock of the dancer's bodies in motion and the larger choreographic patterns. Everything possible is done to allow the camera to preserve the spatial integrity of the dance within the framework of the small screen.

The dancing itself - by such NYC Ballet stalwarts as Suzanne Farrell, Patricia McBride, Kay Mazzo, Karin von Aroldingen, Merrill Ashley, Peter Martins, Robert Weiss, Daniel Duell, Bart Cook, Adam Luders and others - is nothing short of breathtaking, and clear evidence of the company's amazing strength at all levels.

There are additional assets. The music is excellently set forth under the baton of Robert Irving, the company's outstanding music director. Edward Villella, one of the company's former reigning danseurs, is a persuasive host, and the script, by New Yorker critic Arlene Croce, is exceptionally literate and illuminating ("only a man who knows how to tell a story can afford to do without a plot," she says of Balanchine). "Choreography by Balanchine" shows how successfully dance can be transposed from stage to TV when style and substance are appropriately matched.