Chicago police and FBI agents started questioning employes of the Chicago Art Institute yesterday, where three paintings by Paul Cezanne, valued at about $3 million, were discovered missing Wednesday from a storage area to which only a few employes had keys.

Museum officials, who were closeted most of the day with police and insurance officials, would not speculate on the theft. "There was not a breakdown in the security system," said spokeswoman Emily Dwass.

With the discovery of the missing Cezannes, another theft at the institute 10 days before, the heist through a skylight of a $1 million Rembrandt in San Francisco and the burglary of another $1 million worth of art in Santa Barbara in November, the issue of museum security is an increasing public concern. Among museum officials, it is a continuing dilemma, but the thefts have created a tremor of fear as museums are reminded so sharply that even the best security is sometimes breached by thieves bent on beating the system.

"Is theft preventable? I don't think there's anything that's really safe," said E. B. Brown, head of security at the Kimbell Art Museum in Fort Worth, Tex., and member of national and international committees on museum security. "But it seems like more are happening lately, and I don't like it." Brown oversees a $250,000 system installed in 1972 that, like most museum systems, is a combination of human beings (guards) and electronic surveillance and alarms.

"When the boards of trustees of museums gather next I can bet one of the first questions they'll ask is about the state of security," said Huntington Block, a Washington insurance executive whose company is one of the leading insurers of art, including the Chicago Art Institute's Cezannes.

In general, security systems in this country's major museums of art are sophisticated, said Lawrence Reger, director of the American Association of Museums. "The technology to develop highly sophisticated systems which are non-obtrusive exists," he said. "The question is, do museums have the funds to invest in them.

"There's no way to prevent thefts totally -- that would inhibit the purpose of a museum. You're always going to have nuts around, trying to steal irreplaceable works of art or defacing them -- that's a fact of life."

It's difficult to get many details about these sophisticated systems because museums are notoriously reluctant to discuss them for fear of encouraging thieves. "It has always been our policy, and is perhaps being even more stringently adhered to now, that there is no talking about the gallery security," said Katherine Warwick of the National Gallery. "It seems to cause a rash of problems." There is confusion also at the apparently contagious quality of art thefts. "They seem to come in rashes," said E. B. Brown. "The only way we could know why is if we put all the details about a theft, from the weather to the type of painting, into a computer. Then we might have some idea why they happen like this."

There is no consensus among art, police or insurance spokesmen as to whether thefts of major works are easy to fence on the black market because they are so valuable, or difficult to dispose of because they are so famous and widely known to be stolen.

"Very few major works of art have not been recovered sooner or later," said James McLaughlin of the Phillips Collection here.

"There's not too ready a market for something so well known," said Block. "Ransom has got to have crossed his (the thief's) mind. Of course, ransom is a word we insurers are not very fond of. But in my experience, the track record is that most pictures stolen are recovered."

Yet others say there is a major black market in stolen pictures, and one firm, the International Association of Art Security in New York, estimates that as many as 15,000 works of art stolen around the world are still at large.

Interpol put out a list of "The Twelve Most Wanted Works of Art" in 1972, and only one has been recovered since then -- Rembrandt's "Flight Into Egypt." Other works on the list include paintings by Jan Brueghel, Peter Paul Rubens, and Thomas Gainsborough, according to an Interpol spokesman.

While the incidence of "major" works of art being stolen appears to be relatively rare, less valuable works are apparently swiped with increasing frequency. The International Foundation for Art Research estimates that 75 percent of the art museums in the country were victimized at least once last year.

And, while "famous" paintings are more likely to be noticed as soon as they come on the market, others are easier to resell, said Gilbert Edelson, lawyer for the Art Dealers Association of America Inc. "If you steal a Picasso lithograph that is one of 200, that's hard to surface," said Edelson. "Nobody really looks at it that carefully."

New York is one of the few -- perhaps only -- police departments to have an "art squad" on its force. The "squad" consists of one detective. Robert Volpe, who is viewed by many as one of the most knowledgeable in the field.

The FBI used to have officers who specialized in art theft, but that specialty was incidental to their routine investigative work, said FBI spokesman Tom Call. One of them was Donald Mason, now an art security expert. "Don was called in when we got a tip or heard of someone who wanted to sell a painting," Call said. "He'd pose as an art dealer and he knew enough about art to know if that painting was authentic or not."

The Art Dalers Association of America Inc. published a monthly bulletin of stolen works, notifying dealers, museums, and police of as many as 90 thefts in each issue.

"Those two thefts (in Chicago and San Francisco) really surprised me," said association lawyer Edelson. "I can't recall anything really major being taken from a major museum. What's happening here may be following what's been happening in Europe -- a whole rash of art-naps."

"I think the rashes occur because it's played up in the newspaper," said McLaughlin. "It's just like bank robberies.... I'd like to see the money aspect played down. Art belongs to the people. Cezanne would have sold a painting for $100. Just because it would now sell for $1 million, does that make it more valuable?"