THE CITY of Chicago stood unaccustomedly in the center of the nation's ballet spotlight for a brief but glorious interval last week, because it was there -- and only there -- that the Royal Danish Ballet restaged the tribute to August Bournonville (1805-1879) originally mounted in Copenhagen last winter.

The event was a personal coup for Chicago arts patron Geraldine Freund, who more or less singlehandedly conceived, engineered and underwrote the Danes' visit, as the fourth installment of her annual "International Dance Festival of Stars" in the Windy City. Prince Georg of Denmark's royal family, Chicago's Mayor Jane Byrne, Gov. James Thompson and Danish Ambassador Otto Borch were among the dignitaries on hand to welcome the company of 81 dancers to the resplendently designed 3,700-seat Chicago Civic Opera House.

August Bournonville? Hard-core balletomanes know the name well, and a good many dance lovers are familiar with "La Sylphide" and the "Flower Festival at Genzano" pas de deux -- the Bournonville works that dot the repertories of major international companies. But aside from this relatively limited circle -- and the Danes themselves, of course, for whom Bournonville is a culture hero on the order of a Goethe or a Mark Twain -- few have heard much about the life and career of this extraordinarily prolific and cultivated dance artist, especially on this side of the Atlantic.

Yet his ballets, the creative outlook and the manner of dancing he promulgated are not only highly pertinent to contemporary concerns, but also still capable of eliciting fervent response among modern viewers, as the Chicago festival once again demonstrated.

Ballet in the United States, like so much of the rest of our culture, is largely conditioned by the melting-pot syndrome, perhaps never more so than in the last 15 years, when dancers and companies have been subject to such a plethora of influences from every corner. It's our great strength, but it's also a source of shortcoming -- a company like American Ballet Theatre maintains the world's most comprehensive repertory, embracing past and present and a welter of national traditions, but at the same time no one style is reproduced without dulterating elements. Maybe that's the single most potent factor in American admiration of the Danes -- they define for us an ideal of stylistic purity and integrity that for all our bigness and expertise eludes our grasp.

The root of the Danes' exquisite stylistic homogeneity is the Bounonville repertoire. Born in Copenhagen to a French father and Swedish mother, Bournonville brought back to his native land the fruits of his training and professional experience in Paris during the formative years of the romantic era in ballet. In the nearly 50 years of his tenancy as ballet master of Copenhagen's Royal Theatre, he not only transplanted what he learned, but established a school of dancing and a repertory of ballets that remain models of esthetic achievement today.

After his death, the legacy of his work was carried forward from generation to generation and protected from deterioration by a succession of devoted pupils and artistic heirs. Only about a tenth of his more than 50 ballets are currently extant, but given the notorious perishability of dance, that is a formidable amount. The Bournonville heritage, moreover, represents the single largest intact remnant of ballet's romantic period, from which otherwise we have only a few staples like "Giselle."

This points to a second reason for contemporary American fascination with the Royal Danish Ballet. In an era so absorbed with the past, we look with awe and longing upon a repertoire so lovingly preserved -- Bournonville is living ballet history. For the Danes themselves, this has been something of a problem as well as a distinction -- their mission as curators has made it difficult for Danish choreographers and dancers to feel themselves in step with changing times, which is one reason why a good many have become emigres. For those outside Denmark, it's all gravy. We have the inestimable benefits of the Bournonville treasury so carefully guarded across the years, and we also reap the harvest of their expatriates -- from Erik Bruhn to Peter Martins, Peter Schaufuss, Helgi Tomasson (Icelandic by birth but Danish trained) and now Ib Andersen, among others. The most celebrated of our Danish imports have been male, which hints at another Bournonville trait that comports so well with contemporary leanings. Though the romantic ballet tradition in general heavily favored ballerinas over males, Bournonville in particular always accorded men an equal place in his ballets.

Finally, there's the vision of a harmonious and ordered moral universe that Bournonville's ballets so characteristically project, beckoning to us like a rainbow through the miasma of anxieties, catastrophes and disclocations that appear to be the lot of our own century. Perhaps the most endearing revelation of the Chicago visit was the three-act story ballet, "A Folk Tale" (1854), prized by Bournonville himself among all his other works and never before staged in this country. The plot (calling to mind Bounonville's friendship with Hans Christian Andersen) concerns the beautiful Hilde, abducted as an infant by trolls who put one of their own, the rambunctious Birthe, in her place. A series of adventures involving elf maidens, magic spells and comic derring-do eventually restores Hilde to her birthright and her human lover, Ove. Though the brooding Ove suggests Hamlet, the dominant atmosphere is that of "A Midsummer Night's Dream." A warmly melodious score. vivacious pantomime and Bournonville's scintillating choreography deftly conspire to sustain an aura of gremlin enchantment.

At the premiere of "A Folk Tale" June 14, Hilde was danced by 23-year-old Lis Jeppesen, who gives every sign of becoming one of the world's ranking ballerinas in very short order. To the quintessential Bournonville attributes of her technique -- gossamer lightness and fluency, buoyantly filigreed footwork and liquescent phrasing -- she added an absolutely disarming spontaneity, dancing as if she'd never "studied" the role, but was inventing it on the spot. One night earlier she'd been equally captivating in the title role of "La Sylphide," partnered brilliantly by guest artist Peter Schaufuss, who also brought his explosive impact to the full-length "Napoli." Though his dancing was typically impeccable, guest artist Peter Martins was oddly phlegmatic Ove in a repeat performance of "A Folk Tale." One the whole the dancing of the troupe through the seven ballets of the festival seemed spirited and able, the women generally more impressive than the men. The hero of the week, in any case, was Bournonville.

The Chicago festival was one-of-a-kind, not to be repeated elsewhere. Negotiations are said to be underway, however, for a Royal Danish Ballet visit in '82 to New York, and possibly Washington as well. In the meantime, Washingtonians will at least have the chance to see Peter Schaufuss in action, when he appears with the National Ballet of Canada in the opening night performance of "Geselle" at the Carter Barron Amphitheatre tomorrow night.