Dennis Chávez Democratic John J. Dempsey Democratic The 1934 United States House of Representatives election in New Mexico was held on Tuesday November 6, 1934 to elect the state's at-large representative.

Incumbent Dennis Chávez decided not to run for re-election and instead opted to run in the concurrent Senate election.

This was the first open seat since 1922.

Dempsey prevailed in this open seat by a narrow 4 point margin.