Due to a loophole in the US constitution, the Vice President would preside over his own impeachment trial
Impeachment in the United States is when the legislature presses formal charges against a civil officer of government for crimes committed in office. These civil officers are often given a trial that is presided over by some other government official.
When the impeachment trial involves a US president, the Chief Justice is required to preside over the Senate trial. In other trials, the Vice President presides in his capacity as President of the Senate.
Due to this unintended omission in the Constitution, however, the Vice President would also have to preside over his own impeachment trial. Guess we all know the result of that trial.