ThinkProgress:

Newsweek reports that in a conversation “secretly tape-recorded by the FBI on June 25, 2006,” Sen. Ted Stevens (R-AK) “discussed ways to get a pipeline bill through the Alaska Legislature with Bill Allen, an oil-services executive accused of providing the senator with about $250,000 in undisclosed financial benefits.” Stevens promised Allen, “I’m gonna try to see if I can get some bigwigs from back here and say, ‘Look … you gotta get this done’.” Two days later, Vice President Cheney undertook the unusual move of writing a letter to the Alaska Legislature urging members to “promptly enact” a bill to build the pipeline.

To summarize: Bill Allen is accused of bribing Ted Stevens to get his pipeline deal approved by the Alaska Legislature. Stevens promised "bigwigs" would help. Two days later, Cheney helped.

Cheney may or may not have been bribed directly, but he participated in a bribery scheme. Former Rep. Bob Ney (R-OH) went to jail for a similar scheme involving Jack Abramoff.

The Constitution is crystal clear on bribery; after treason, it is the gravest possible offense:

The President, Vice President and all civil officers of the United States, shall be removed from office on impeachment for, and conviction of, treason, bribery, or other high crimes and misdemeanors. 

So when will Congress impeach Dick Cheney?