American 'Nicholas Nickleby' is a triumph of regional theater; Nicholas Nickleby. Great Lakes Shakespeare Festival musical production based on the Charles Dickens novel. Directed by Robert Lanchester and Edward Stern. Starring David Purdham.

This version of the widely touted musical, done previously on Broadway by the Royal Shakespeare Company, is no stopgap substitute. It is a brilliant evening in the theater in its own right. That it is an American troupe is cause for pride. That it is a regional theater is cause for celebration.

Having recently completed its run here, the show will begin a Chicago engagement of at least eight weeks on Dec. 1 - and then perhaps go on to other cities.

Meanwhile, the chance to see this fully staged production of ''The Life and Adventures of Nicholas Nickleby'' was sufficient to lure one to Playhouse Square here. Once the core of Cleveland's entertainment scene, it contains five theaters in roughly one city block, three virtually sharing common walls, and a fourth very near by.

By the early '60s, decades after vaudeville had failed, large-screen theaters became unprofitable and the houses here were closed. Several went into total disrepair under neglect and vandalism.

Now, an ambitious restoration project is under way that will restore three of the four theaters - the State, the Ohio, and the Palace - to their original glory as the forums for plays, musicals, opera, ballet, and star entertainment.

The Ohio is the first theater to be finished, and it has become the permanent home of the Great Lakes Shakespeare Festival, a 20-year-old regional troupe that has acquired quite a reputation for itself. Certainly, any company that would lay out $500,000 to mount so madly ambitious an event as ''Nicholas Nickleby'' had to expect that the community it serves would support it well.

The company won the first rights to the play after Broadway - quite a feather in regional theater's cap. ''Nicholas Nickleby'' became just as much an event in Cleveland as the Royal Shakespeare Company production had in New York, but with a difference. The two-evening, 81/2-hour affair cost $100 in New York and only $ 40 in Cleveland.

Not only was ''Nicholas Nickleby'' embraced avidly by Clevelanders (four extra performances were added, and they sold out almost instantly), but many other cities besides Chicago have expressed an interest in getting the production. Vincent Dowling, producing director, and Mary Bill, managing director, have every reason to be bursting at the seams with satisfaction. That Cleveland should have such a splendid troupe speaks highly of the city, and of the arts mavens who support and nurture such an endeavor.

David Edgar's feat in paring down nearly 900 paperback pages of dense sprawling Dickens to nearly eight hours of stage time is now theatrical history. In true Dickensian style, he presents a composite of vignettes, tied together by the thread of the saga of the Nickleby family - Nicholas, his mother, his sister Kate, his cruel, venal Uncle Ralph. The story takes the viewer to London, Yorkshire, and Portsmouth, and of course back to London several more times.

In Cleveland, Robert Lanchester and Edward Stern divided the directorial duties of the production, taking an equal number of scenes, working on them separately, uniting them in the closing weeks of the rehearsal period. It is testament to their ability to work together that there is nary a glitch that tells the viewer who directed which scene. Their work is full of magic, as in Nicholas's departure from London atop a stagecoach - a memorable moment.

The scope of the production is astounding. Forty-six actors perform some 300 roles, in 96 scenes, handle 800 props, and stand about in 500 light cues. The two directors accumulated some 500 hours of rehearsal over six weeks.

On John Ezell's rambling framework unit set, with overhead ramps stretching into the balcony, each scene takes a special flavor - now a foggy London street, a frigid Yorkshire attic, a stuffy cramped parlor during a rousing party - thanks to the nonspecific look of this handsome set.

The action often spills out into the audience, and by show's end, the audience feels it knows each character as at least an acquaintance, if not a friend. The Lewis D. Rampino costumes are innumerable, always striking. Toni Goldin's lighting is of the caliber one expects on only the finest theatrical stages.

This was all to be expected. The technical side of most top regional theaters is of an unusually high standard these days. What was not really expected was the consistency of acting, from the principal players to the youngest apprentice - for regional theater, an almost unheard-of level of quality. (It is even a superior average for some Broadway productions of the recent past, or some of the better festival stages in North America.)

David Purdham's Nicholas is all innocent amazement, poise, and sensitivity. Maggie Thatcher's Kate is at once decisive, forceful, and beguiling. Sara Woods makes Mother Nickleby an amusingly loquacious fuddy-duddy with a heart of gold. Bob Breuer consistently portrays Ralph's domineering sinister venality. Richard C. Brown captures the audience's collective heart as the nobly motivated Newman Boggs.

In various other roles, Jeannine Hutchings, Helena Carroll, William Youmans, Leta Anderson, Bernard Kates, and Reuben Silver stand out even in so excellent a company.