Cheney, 46, said she will run in the Republican primary next year against incumbent Mike Enzi, 69, Roll Call reported.
"Over the last several years citizens across our great state have urged me to consider running for the Senate in 2014," Cheney said in announcing her candidacy. "As I've traveled to every corner of Wyoming, seeing old friends and meeting new, I've been honored to have the chance to speak with so many of you about your concerns, your fears and your hopes for the future.
"... Today I am launching my candidacy for the United States Senate."
Enzi said Tuesday he will be going after a fourth term.
"I intend to run for re-election for Wyoming's Senate seat in 2014," Enzi said in a statement. "In the meantime, I will do the job I was already elected to do. My trips to Wyoming almost weekly, the public listening sessions, the groups I meet with and speak to, working behind the scenes -- this is what I have been doing since I was elected and this is what needs to be done."
Cheney, whose father represented Wyoming in the U.S. House, is a lawyer and political commentator who has been active in the Republican Party. She held several positions in the U.S. State Department during the administration of President George W. Bush.
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