The Federal Communications Commission gave American Telephone & Telegraph Co. the go-ahead yesterday to build the first commercial "cellular" mobile radio system in the United States.

In its first approval of a construction permit for this revolutionary portable telephone system, the commission unanimously turned aside objections that its approval would give the telephone company, which will build the system in Chicago, an unfair advantage over competitors that also want to offer cellular service in that city.

Saying it was in the public interest to get the new service in operation as soon as possible, the FCC said it would not hold up AT&T's application pending a future commission decision on what other company should receive government approval to operate in Chicago.

The commission said, however, that once AT&T builds its system, the FCC may order the company to delay starting its commercial operations for at least six months to give competitors a chance to get their systems off the ground.

The FCC's action was the first that it is expected to take over the next three months on the nearly 200 applications that have been filed to operate cellular systems in the nation's largest 30 cities. More applications -- numbering in the hundreds -- are expected to be filed within the next three months for other U.S. cities.

There is intense interest and competition for this new service, which is regarded as a highly lucrative venture. Unlike the current mobile telephone service, which allows only 20 users to speak simultaneously, the cellular system permits thousands of users to speak at one time, through the use of low-power transmitters and computers.

In approving the new service, the FCC has decided to grant two cellular licenses for each city -- one to a telephone company and the other to a nontelephone company.

Competing for the nontelephone license in Chicago are Rogers Radiocall Inc., a joint venture of Rogers Radiocall Communications Services Inc. and Metromedia Inc., and Cellular Mobile Systems of Illinois Inc., a subsidiary of the Graphic Scanning Corp. Under FCC's decision yesterday, these two firms will have to undergo lengthy hearings to determine which is more qualified to build the second system in Chicago.

The FCC ordered the hearing even though the commission may ultimately declare CMS unfit to hold a cellular license. That ruling could occur if a pending investigation into CMS's parent upholds allegations that Graphic Scanning improperly set up four shell companies to obtain extra radio paging frequencies.

A ruling that CMS is unfit could hurt Graphic Scanning's plans to offer cellular service in all the nation's top 30 cities, including Washington and Baltimore.

Competition for the nontelephone rights in this area narrowed this week when two of the four competitors announced they would merge their applications.

Metropolitan Radio Telephone Systems Inc., a cellular radio telephone consulting firm, and Metro Phone Associates, a partnership of Metrocall of Virginia Inc., which is one of the area's largest paging and radio telephone companies, and Metromedia Telecommunications Inc., which owns a television station, and two radio stations in the area.

The merger is the second for the area, coming just two months after two other competitors for the same market merged. The Washington Post Co. and American Radio-Telephone Service Inc., which is operating an experimental cellular system here, agreed to merge their applications in September.