The town hall was interrupted several times by protesters.
The activists are fellows from the Republican Leadership Initiative.
"The first and foremost priority is to fix the unlawful immigration," the senator said.
Donald Trump is in a dead heat with Democratic nominee Hillary Clinton in South Carolina.
Trump is debating softening his immigration proposals.
The public, unsecured network mocks Clinton's email controversy.
The criticism comes amid questions over the GOP nominee's position on immigration.
"We must get to the bottom of what looks like a pay to play scheme,” Christie said.
OPINION | No other politician has had such an impact simply by being
"Who wants those [bad] people thrown out?" Trump asked.