United Airlines announced plans yesterday to offer service between Dulles International Airport and Chicago's O'Hare Airport--a move hailed by Dulles advocates as a major gain for the long-underused airport.

"The trend is moving in the right direction," said Thomas Morr, president of the Washington Dulles Task Force, a group pressing for expanded service at Dulles. Dulles has long been overshadowed by its more heavily used rival, National Airport.

By scheduling three Dulles-O'Hare round trips a day, United matched a recent move by American Airlines and signaled a dramatic increase in service from Dulles to Chicago, a key hub, or connecting point, for air service.

A year ago, officials said, Dulles' only daily flight to Chicago was a single one-way trip on Northwest Orient Airlines. Then on May 24, Northwest Orient added two daily round trips to Chicago from Dulles, they said.

Nine days ago, American Airlines started providing three Dulles-O'Hare round trips a day. United's Dulles-O'Hare service will begin April 24.

"Chicago's gone from zero to nine in one year," Ronald M. Smith, United's Mid-Atlantic regional vice president, said at a luncheon held to announce the new flights, which include a new daily round trip to Philadelphia.

Nevertheless, United officials cautioned against interpreting their plans as an attempt to transfer flights to Dulles from National or Baltimore-Washington International Airport, which also competes with Dulles for air service.

"We're not robbing Peter to pay Paul," said John Philp, special assistant to United's chairman. "We don't view this as a shift in resources that would downgrade our service at National or BWI. It's not a shift of focus."

Smith said United would soon announce new service at National and Baltimore-Washington airports. He did not elaborate. When American started its flights to Chicago from Dulles, it also added two additional round trips to O'Hare from National and Baltimore-Washington.

About 2.6 million passengers used Dulles last year, a 12 percent increase over 1981. The total, nevertheless, remained far short of the 3.5 million passengers in 1979, Dulles' busiest year. Officials said growth was especially pronounced in the last months of 1982, a promising sign for the airport.

Meanwhile, National, hurt by the economic recession and the air traffic controllers' strike, has shown a steady decline from 15.1 million passengers in 1979 to 13.2 million last year. Federal officials are considered likely to restrict the number of passengers allowed at National to about 15 million from its current ceiling of 16 million passengers, a shift expected to dampen growth there.

Baltimore-Washington airport has reported a 20.2 percent increase in passengers to nearly 4.6 million last year after two years without significant gains. Carroll Hynson, the airport's information and trade development director, said that 30 percent of its passengers are estimated to come from the Washington area, a marked rise from about 20 percent several years ago.

Dulles advocates cite several factors as indications of the airport's promise, including continued population increases in western Fairfax and Loudoun counties.

The recent opening of a 10-mile section of Rte. I-66 between the Capital Beltway and the Theodore Roosevelt Bridge has shortened driving time to Dulles, officials said, and travel to Dulles is expected to be reduced further next fall when a highway extension is scheduled to link I-66 with the Dulles Access Road. "It will be a big boost for Dulles Airport," said Dulles task force President Morr.

Officials also said improvements are expected in bus and limousine service to Dulles from downtown Washington and other metropolitan area points as a result of plans being reviewed by the Federal Aviation Administration, which owns Dulles and National.

The Washington Dulles Task Force, which is financed by federal and state agencies and contributions from businesses, is conducting a stepped-up campaign to promote the airport. Earlier this week, the task force announced the hiring of a Washington-based advertising firm, Henry J. Kaufman & Associates Inc.