Bill Paxon (a former representative from New York) and Bob Dole were mentioned over the weekend as possible candidates for Speaker of the House. Neither one is currently a member of Congress. Is that allowed?
The answer is yes, though it would be a historical first.
The Constitution gives the House of Representatives the right to "chuse their speaker" but doesn't specify a procedure. This means every session of the House must first decide how to choose a Speaker before it can actually choose one.
Traditionally, Congress has adopted the following procedure (proposed by Thomas Jefferson). First, the party caucuses each vote to select a candidate. Second, the entire House votes on the two nominees. Since House members invariably vote along party lines in these elections, the majority candidate always wins. Thus the really important election is the nomination vote within the majority caucus. And House rules do not require that a nominee be a member of Congress.