Richard graduated from Bridgewater College in Rockingham County, Virginia and was admitted to the Virginia Bar. He was a delegate to the Republican National Convention in 1964. In that same year, he ran for the House of Representatives in based in Richmond, facing Democratic State Delegate David E. Satterfield III. Obenshain nearly ended the long run of Democratic dominance in the district, losing by only 654 votes. He nearly won on the strength of Barry Goldwater carrying the district; Goldwater won every county-level jurisdiction in the district except for the city of Richmond. However, Republicans had been making inroads among Byrd Democrats for some time before then. As early as the 1930s, several Byrd Democrats had begun splitting their tickets for national elections due to the increasingly liberal bent of the national party.