I am assuming (and you know what happens when you assume) you mean the SuperBowl that was played in 1986 and not Superbowl MMLXXXVI, which will take place roughly 1,940 years from now.
The Chicago Bears won Superbowl XX, played on January 26, 1986.
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The Oakland Raiders, The Oakland Raiders won the Super Bowl in January of 1981, but it was from the 1980 season. This answer could actually be answered as the San Fransisco 49ers who won the Super Bowl in January of 1982, but it was from the 1981 season.
The Oakland Raiders beat the Philadelphia Eagles 27-10 in Super Bowl XV played on January 25, 1981.