Kill Trump's third-party threat: Republican Party chief wants all GOP candidates to pledge not to run as independents – but only one might Republican National Committee chairman Reince Priebus says every GOP White House hopeful 'should pledge not to run as a third-party candidate' He was responding to threats from front-runner Donald Trump to undercut the party if Priebus and others don't show him more respect 'I think everyone understands that if Hillary Clinton's going to get beat, she's going to get beat by a Republican,' Priebus said Trump walked back the notion of a break with the party after...