UCLA alums have now won MLS titles in each of the last 10 seasons.
Edwards Jr. and Stolz earn first-team honors; Chavez named to the second team.
Senior captain becomes the second straight UCLA men's soccer player to earn honor.
Junior midfielder led the team with 30 points and 11 goals this season.
UCLA falls 3-3 (5-4 on PKs) as it concludes its season at 12-3-5.