The players were suspended from the tour for their involvement with the Saudi-backed league.
The complaint was filed in the United States District Court for the Northern District of California.
The filing alleges that the restrictive policies of the PGA are an attempt to choke off the supply of professional golfers to LIV.
They are asking that their suspensions be lifted. Gooch, Hudson, and Matt Jones are asking for a temporary restraining order against the Tour so they can play in the FedEx Cup playoffs.
The suspended players are now working for the Saudi Golf League and want to return to the tour. It compromises the TOUR and the competition, to the detriment of our organization, our players and our partners.
Lefty was suspended by the tour in March for recruiting players. In June, the tour denied the appeal of the decision and barred 16 additional players from participating in league events for playing in the LIV golf tournament without getting the proper media clearances.
While acknowledging the human rights offenses surrounding the Saudi kingdom, Lefty has defended LIV Golf as a necessary disruptor of the tour.
The lawsuit states that the PGA Tour is an entrenched monopolist with a vice-grip on professional golf and that it is trying to defeat competition.
According to the complaint, the PGA Tour threatened sponsors, vendors and agents to force players to leave LIV Golf, which is funded by Saudi Arabia.
The players brought this action to vindicate their rights as independent contractors and to challenge the PGA's anti-competitive rules. Golfers should be allowed to play golf despite the efforts of the PGA Tour.
The Justice Department is looking into possible antitrust violations related to LIV Golf.
The Saudi league has been pushed for opposition by the PGA Tour.
The report was contributed to by CNBC's Dan and Kevin.