What government body has the right to impeach?

The US Senate.

The House of Represent brings impeachment charges. If a simple majority of the House votes for impeachment, the official proceeds to trial in the Senate. Removal from office requires a two-thirds vote of the Senate.

The United States Senate has the sole power to try all impeachments. When the President of the United States is being tried, the Chief Justice shall Preside. This can be found in the U.S. Constitution Article 1 Section 3. At all other impeachment trials, a committee of Senators act as a panel of judges. This practice began in 1986 when the Senate amended its Rules and Procedures for Impeachment Trials.