Halliburton is the oil equipment company that Cheney used to run before he become VP. He STILL receives a 'stipend' from them which is basically equal to the salary he gets as the VP (in the 100 thousand range). Halliburton is under investigation for various contract violations, such as overcharging in Iraq, no-bid contracts (aka, they were just handed the contract. Total contracts to them are about $20 billion!), violation of international sanctions in Iran, Libya, and other countries, and a number of other questionable actions.
There has not been any proven direct correlation between Cheney's actions as VP and Halliburtons contracts, but if a connection is proven, this could easily fit into the category of 'high crimes'... aka treasonable and impeachable actions.
Please note that Cheney also had energy policy meetings early in Bush's presidency about He meet with people from energy companies including Halliburton and Enron, and excluded other groups (aka, those without corporate interests) These meetings were behind closed doors, and information about them have not been released to the public. There have been lawsuits to find out what happened in those meetings, but Cheney has been refusing to release any information about these meetings because of 'executive privilege'.
One recent bit of news about Cheney apparently serving in the interest of Halliburton is here
