CODY, Wyo. (Reuters) - Liz Cheney, former Vice President Dick Cheney’s eldest daughter, claimed victory late on Tuesday in Wyoming’s Republican primary race for the state’s lone U.S. House of Representatives seat. Unofficial early results by 10 p.m. (0400 GMT) showed Cheney with 26,363 votes in the nation’s least populous state. State Senator Leland Christensen was running a distant second, with almost 15,000 votes, while her six other Republican competitors each held fewer than 12,000 votes. “I’m honored by the trust Wyoming Republicans have placed in me to serve as our next Representative in Congress,” Cheney said in a statement. The Casper Star-Tribune newspaper called the race late on Tuesday night. Wyoming is a reliably red state, with the Republican primary winner all but assured of a general election victory in November. Cheney’s apparent victory comes two years after she launched an unsuccessful bid for a U.S. Senate seat that saw her withdraw from the race early. She drew criticism from some establishment Republicans two years ago when she ran against popular incumbent Senator Mike Enzi and was labeled a “carpetbagger” for having only recently established residency in Teton County, one of the country’s wealthiest zip codes, in a state widely populated by working-class miners, oil, and gas workers. She said a family health crisis prompted her to withdraw. Cheney, 49, is a lawyer who worked in the U.S. State Department while her father was vice president. Her campaign has received strong financial support from former high-ranking government officials, such as former Presidents George H.W. Bush and George W. Bush, former Defense Secretary Donald Rumsfeld and former White House political adviser Karl Rove. Cheney campaigned as a “strong conservative voice for Wyoming,” promising to protect the state’s pivotal coal industry, defend gun rights, and generally work “to reverse President Obama’s devastating policies.” 