A special election was held in Massachusetts's 1st congressional district on October 23, 1820 to fill a vacancy created by the resignation of Jonathan Mason (F) on May 15, 1820. As a majority was not achieved on the first ballot, a second ballot was held November 6, 1820
Election results
Gorham took his seat on November 27, 1820.
References
Massachusetts's 1st congressional district special election, 1820 Wikipedia(Text) CC BY-SA