Presumptive Republican nominee Donald Trump holds a tenuous lead over former Secretary of State Hillary Clinton in Texas, a solidly red state.

According to a new poll by the University of Texas/Texas Politics Project, Trump leads Clinton by only 8 percentage points (41-33) in Texas, which has voted Republican in every presidential election since 1980. Nineteen percent say they prefer someone else, and 8 percent are undecided.

Trump's 8-point lead in a head-to-head matchup with Clinton shrinks by 1 point when also polled against former New Mexico Gov. Gary Johnson, who is the Libertarian nominee. Then, Trump leads with only 39 percent to Clinton's 32 percent, while Johnson pulls in 7 percent.

Trump's lead is slimmer than the margins won by 2008 GOP nominee John McCain and 2012 nominee Mitt Romney. McCain topped then-Sen. Barack Obama by a 12-point margin, while Romney took home the Lone Star State by 16 points.

Texas was also one of the few states Trump was unable to bag during the primary contests. Trump lost the state to Texas Sen. Ted Cruz, who won with nearly 44 percent backing to Trump's 26 percent. However, Trump has continued to campaign there, and held events in Dallas and Houston within the past two weeks.