Allie Quigley led Chicago with 26 points, while Candace Parker added 16 points and 13 rebounds in the championship-clinching victory.
The sixth-seeded Sky are the first team in WNBA history to win the championship without being seeded first or second.
Their eight wins are the most in WNBA postseason history, after winning two single-elimination games to reach the semifinal round, where they won three games against the Connecticut Sun.
The WNBA Championship Trophy is awarded to the team that wins the best of five games. The Phoenix Mercury won Game 2 of the finals.
Of the 12 WNBA teams that compete during the regular season, eight teams, regardless of conference, qualify for the postseason playoffs.
The Houston Comets, the Seattle Storm and the Minnesota Lynx have each won four championships since the playoffs began in 1997.