In a four-way poll of registered voters, Trump garnered a weighted 41 percent support and Clinton drew 38 percent — with a 3 point margin of error. Libertarian nominee Gary Johnson had 4 percent support and Green Party nominee Jill Stein saw 1 percent.
Other recent Texas surveys have shown Clinton pulling closer to Trump: A recent SurveyMonkey poll even showed a two-point race in the state.
According to a release accompanying the University of Houston results, every GOP candidate has carried Texas by at least 11 percent since 2000. In 2012, Republican nominee Mitt Romney defeated President Barack Obama 57 percent to 41 percent.
Trump's struggles in Texas are mirrored in his campaign's floundering poll numbers in national surveys and in other traditionally Republican states like Alaska.
"The national gains Hillary Clinton has made in the last two weeks are evident in Texas, where she has closed within three points of Donald Trump," Richard Murray, professor of political science and director of the Hobby School's Survey Research Institute, said in the release. "With such a close margin, the key question will be which candidate can actually get their supporters to the polls over the next three weeks."
In a move demonstrating her campaign's confidence, Clinton's team purchased a modest one-week ad buy for some parts of Texas — an unusual move for a Democratic presidential nominee.