Walter Dulany Addison was an Episcopal clergyman who served as Chaplain of the United States Senate (1810–1811).

The chaplain of the United States Senate opens each session of the United States Senate with a prayer, and provides and coordinates religious programs and pastoral care support for senators, their staffs, and their families. The chaplain is appointed by a majority vote of the members of the Senate on a resolution nominating an individual for the position. The three most recent nominations have been submitted based on a bipartisan search committee although that procedure is not required.