You can watch the entire prayer below, courtesy of the Associated Press.
In addition, the International Campaign for Tibet reports on the event and the rest of His Holiness’ visit to Capitol Hill. Here’s a snippet:
The day began with the Dalai Lama serving as guest chaplain in the Senate chamber. He offered a prayer from “A Guide to the Bodhisattva’s Way of Life by the Buddhist master Shantideva, which he said was his favorite. He devoted his prayer to “Buddha and all other gods.” Sen. Mark Warner (D-VA) welcomed his call to “help dispel the misery of the world” …
The office of the Senate Chaplain said it was probably the first time that a Buddhist had given the opening prayer in the body. It is also almost certain that His Holiness’ prayer marked the first time the Tibetan language was spoken on the floor of the Senate.