The Republican New Jersey governor is favored by 44 percent of those in the swing state while the former secretary of state is supported by 41 percent, the Quinnipiac University poll said in a statement.
Potential Republican candidates fared better than possible Democratic rivals in two other hypothetical match-ups, the poll found.
Marco Rubio was a slim favorite over Clinton. Some 46 percent of those asked preferred the Florida senator compared to 45 percent for the former first lady.
Both Christie and Rubio were favored over Vice President Joe Biden. The poll said Christie would top Biden 48-32 percent and Rubio would come in ahead 48-35 percent.
Hillary Clinton was the favorite among women against either Republican. She was preferred 49-38 percent over Christie and 53-38 percent against Rubio. Men preferred the GOP possibilities.
The "very early numbers" reinforce the perception of Colorado as an important swing state in presidential politics, said Tim Malloy, assistant director of the Quinnipiac University Polling Institute.
The poll interviewed 1,065 registered voters June 5-10. The margin of error was 3 percentage points.