Now that the Navy has almost finished building the world's biggest and costliest submarine, the $1.5 billion Trident, it is spending $4.4 million to dredge a channel to make sure that the giant can reach the sea.

The 3.8-mile channel being deepened is in the Thames River, running between the Electric Boat Division yard at Groton, Conn., where the Trident is being built, and Long Island Sound.

Two years ago when The Washington Post reported that Trident was in danger of being built too big to fit through the door, Electric Boat and Navy spokesmen said they should solve the problem by putting only a partial load in the submarine so that it would float higher in sailing out the channel. l

Subsequently, however, the Navy decided to dig the channel four feet deeper, making it 40 feet. The Navy said the dredging will be finished by May 31.

The deeper channel, according to the Navy "enlarges the margin of safety and allows greater flexibility in scheduling transits" between the shipyard and the sea.

The first Trident -- which is 560 feet long, or five feet longer than the Washington Monument is high -- was originally scheduled to be completed last April. The revised date became next Nov. 30, and the new one is Feb. 1, 1981. The latest slippage, the Navy said, was caused by the need to replace one of the sub's turbines.