Hillary Clinton has a chance to turn Missouri blue in November, according to a new poll that shows the Democratic presidential nominee virtually deadlocked with Donald J. Trump in a state that Republicans carried easily four years ago.

A survey from Monmouth University found that 44 percent of likely voters supported Mr. Trump and 43 percent backed Mrs. Clinton. Gary Johnson, the Libertarian Party’s nominee, who barely registered in Missouri when he ran in 2012, received support from 8 percent.

The close race in Missouri underscores the challenge facing Mr. Trump, who needs to carry the states that Mitt Romney won four years ago while flipping others to defeat Mrs. Clinton. Mr. Romney won Missouri by nearly 10 percentage points in 2012 on the back of strong support from white voters. Senator John McCain narrowly beat then-Senator Barack Obama in Missouri in 2008, and no Democrat has won the state since Bill Clinton carried it in 1996.

This year, Mrs. Clinton holds a strong advantage among minority voters in the state and is trailing Mr. Trump by only 13 points among white voters, with the Republican nominee surprisingly doing better with white women than white men.