But Clinton, a Democrat, holds a strong lead against eight other potential Republican contenders, the CNN/ORC International poll shows.
Christie, who won re-election in a landslide last month, leads Clinton nationally among registered voters 48 percent to 46 percent, the poll results indicate.
The 2-point difference is within the poll's 3-point error margin.
Christie "performs particularly well among independents, winning nearly six in 10 in that key group," CNN Polling Director Keating Holland said.
"He also wins a majority of suburbanites and older voters, something that no other GOP hopeful tested was able to do against Clinton," he said.
"Christie doesn't win in the Northeast, although he does hold Clinton to a bare majority there, but he has a solid edge in the Midwest, while playing Clinton to a draw in the South and West," Holland said.
Christie has a 14-point lead among men but trails Clinton by 10 points among women, the poll shows.
Neither Christie nor Clinton has announced intentions to run for president, but both have expressed a possible interest and are widely considered strong potential candidates.
Clinton is far ahead of several other possible GOP presidential hopefuls, the poll suggests.
She is ahead of House Budget Committee Chairman Rep. Paul Ryan of Wisconsin, last year's GOP vice presidential nominee, by 8 percentage points.
She beats Sen. Rand Paul of Kentucky by 13 points and former Arkansas Gov. Mike Huckabee, a 2008 GOP presidential candidate, by 15 points.
Texas Gov. Rick Perry, who ran for the 2012 Republican nomination, is 17 points behind Clinton; Sen. Ted Cruz of Texas trails by 18 points, former Sen. Rick Santorum of Pennsylvania, who finished second to eventual 2012 GOP nominee Mitt Romney, and Sen. Marco Rubio of Florida are both 19 points behind, and former Florida Gov. Jeb Bush is 21 points behind Clinton.
"Keep in mind that polls taken so many years before an election have little or no predictive value," Holland said.
The CNN phone poll of 950 registered voters was conducted by Opinion Research Corp.'s ORC International Dec. 16-19.