Law's play helped the White Sox win their division and get to the 1983 American League Championship Series, the franchise's first postseason appearance since 1959. He was one of the few Sox position players who came through in the ALCS, going 7-for-18 at the plate (.389) and stealing two bases. The team managed to score just three runs in the entire series and lost it to the Baltimore Orioles, three games to one.