"There have been complaints about access, water on the trail and cleanliness," Chaffetz said.
Sen. Orrin Hatch, R-Utah, introduced similar legislation in the Senate.
Loyal Clark, Uinta-Wasatch-Cache National Forest spokeswoman, said the forest service is still reviewing the Chaffetz proposal.
And a BYU spokesman said a change in ownership will not restrict access to the Y, a popular hiking destination.
"Nothing will change for the public," said Todd Hollingshead. "They will still be able to access it as in the past."
Chaffetz said BYU owns the lower half of the Y trail going up to the mountain, but the Y and the upper half of the trail are on forest service property.
Clark said the forest service issues BYU a special-use permit allowing it to maintain the Y.
Chaffetz said there have been some problems with litter on the trail, as well as a lack of water for hikers. He said the last time he hiked the trail he saw garbage, but said it was an overall positive experience.
He said BYU would have more resources for maintaining the trail than the forest service, which he said is stretched thin.
Clark said the forest service uses volunteers to help maintain trails on forest service land.
Chaffetz's bill is co-sponsored by Reps. Eni Faleomavaega, D-American Samoa; Jeff Flake, R-Arizona; and Howard "Buck" McKeon, R-Calif. All three are BYU alumni.
Hatch's bill is co-sponsored by Sen. Mike Lee, R-Utah, and son of former BYU President Rex E. Lee.
Salt Lake civil rights attorney Brian Barnard saw no constitutional problem with selling the forest service land to BYU, which is owned by The Church of Jesus Christ of Latter-day Saints.
"But such displays are rather ugly," Barnard said in an email. "Perhaps the federal government might sell 80 acres to Nu Skin [Enterprises]."
The block Y
BYU's block Y, which stands at the 6,200-foot level of Y Mountain, was built in 1906. BYU President George Brimhall wanted to have all three letters emblazoned on the side of the mountain. So a bucket-brigade of students hauled the sand, rock and lime up the mountain to make the Y, which was done first to serve as the reference point for the other letters. But the task proved so arduous that the university abandoned plans for the B and U.
The Y, now covered in concrete, stands 380 feet high and 130 feet wide.
The Y is illuminated five times a year: freshman orientation, homecoming, Y Days and graduations in April and August.