LOUIS SULLIVAN; His life and Work. By Robert Twombly. Elisabeth Sifton/Viking. 530 pp. $29.95.

GROWING UP in Chicago, if you have your wits about you and keep your eyes open, there comes a time when you realize you're living in a pretty remarkable place. Whatever else it is, Chicago is a kind of living, breathing, working architectural museum. The work of three of the most important architects of the past 100 years -- Ludwig Mies van der Rohe, Frank Lloyd Wright, and Louis Sullivan -- is there in an abundance not to be found in any other city.

Mies is all over the place. Although relatively few in number, his buildings are big and can't be missed. Wright's houses are there around the city and the western suburbs; just ask, and you'll have them pointed out to you. But Sullivan's buildings, although fairly numerous, are a little harder to search out; you'll need a book to help you -- one such as this biography of the architect and critical guide to his work by Robert Twombly.

The reason Louis Sullivan's buildings are more difficult to find is that he did his work much earlier than the other two. His years of triumph fell in the 1880s and the first few years of the 1890s. Some of his best buildings have by now, of course, fallen to the wrecking ball. And except for the recently (1967) renovated Auditorium Building, perhaps his finest, most of the rest are obscured by the gray urban clutter of the Loop and near-south side. The city has grown up around them. Those that once stood out, proudly dominating the urban landscape, are now dwarfed and partially hidden by buildings that are merely taller.

Sullivan was also the least "modern" in spirit of the three. Although his buildings, both those of masonry and steel-frame construction, were structurally very sound, Sullivan excelled at decoration and rich beauty of shape. Even today, sometimes under deep layers of soot, their elegance can be distinguished in the design details that found their origin in his famous dictum, "Form follows Function."

Louis Sullivan was the son of immigrant parents, his father an Irishman and his mother French Swiss. If not artists, his parents were both artistically inclined, his mother an excellent pianist and his father a fiddler and dancing master. (Sullivan's Irish grandfather had been a landscape painter.) Their ambitions for him sent him on to schools they could barely afford -- Massachusetts Institute of Technology and L'Ecole des Beaux-Arts in Paris. Once in Europe, he traveled to Rome and saw the Sistine Chapel ceiling. Michelangelo electrified him and changed his life on the spot. He decided that the Ecole had nothing more to teach him and returned to America, where a job was waiting for him at an architectural firm in Chicago.

IT WAS a city ripe for a talent such as his. The Chicago Fire of 1871 had leveled the heart of the city as it then was; but with money rolling in from all over the Midwest, Chicago was rebuilding quickly and quite impressively when Sullivan became active as an architect and designer in 1875. And when, five years later, he joined the firm of Dankmar Adler as a junior partner, his star began to rise rapidly.

Adler was the perfect partner for the young esthete. Already established as an architect, he had a firm grasp of engineering (one of the first in the world to know anything about acoustics), and was a good businessman who dealt well with clients. All these were talents in which Sullivan was at least somewhat deficient. He was left free to do what he did best -- design. The Grand Opera House, and particularly the six-story Borden Block of offices, which were the first commissions he worked on for Adler, show his work particularly in the decoration and ornamentation for which he became so famous.

The firm was kept very busy designing structures of all sorts, from private homes to large commercial buildings and theaters, while Louis Sullivan rose to full partner. The Ryerson Building, the Troescher Building, the McVickers Theatre Building all went up and were marvels in their day. But for the firm of Adler & Sullivan, they were as preliminaries to the main event -- the Auditorium Building, a commission they accepted in 1886. It was not just the biggest building Chicago had seen up to that time ("containing 136 offices and stores, four hundred rooms and other hotel facilities, a forty- two-hundred-seat theater, and a five-hundred seat recital hall"), at $3.2 million, it was also the most expensive, and quite simply it was also the best. To do the job, it was necessary for Adler & Sullivan to hire a large troop of junior designers and draughtsmen. Among them was Frank Lloyd Wright, on whom Sullivan had great professional and personal influence.

When the massive building was dedicated in 1890, it "was the biggest thing to hit Chicago since the 1871 fire." The firm was famous, and Louis Sullivan was an architect-celebrity. But it was for both the beginning of the end, because the depression of the Nineties put a firm brake on building in Chicago and the rest of the country. From 1893, Adler & Sullivan barely scraped by, and in 1895 the partnership dissolved, Dankmar Adler taking what amounted to an early retirement. It led to ill feeling between them, and when Adler came back to the practice of architecture in less than a year he did so independent of Sullivan.

Louis Sullivan was 39 when Adler left the firm. With a few hills rising from the valleys, his life charted a downward course from that point on. His biographer, Robert Twombly, does a good, workmanlike job up to that point, but in describing Sullivan in decline he does much better. Where before, Twombly had merely presented his subject for our scrutiny, he now analyzes the personality traits that made it apparently impossible for Sullivan to succeed without the support of his partner. Eventually, at a time when his professional fame continued unabated, he simply could not get work. He entered into a late marriage with a much younger woman that proved disastrous -- not surprising, since there is good reason to infer, as Twombly does here, that Sullivan was homosexual.

It is a sad story. By the time he died at the age of 67, he was not quite broken, for he had recently published his autobiography, which was characteristically arrogant in tone, and he was still scrambling desperately for commissions. But he was forced to live off handouts from Frank Lloyd Wright and other old associates. It seems sort of a Hollywood story, doesn't it -- one reminiscent of the career of D.W. Griffith? Perhaps that's not so strange, for film directors and architects are the only artists who must have the investment of huge sums of money from others to practice their art. And once the money people stop believing in you, for whatever reason, you're one of the living dead.