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The blast killed a security guard and two truck drivers delivering supplies, according to Abdul Qayoom Baqizoy, the provincial police chief.
Six civilians suffered injuries, he said.
The Taliban claimed responsibility for the attack, which occurred after a minibus stopped at the gate for a security check.
In an e-mail, a spokesman for the terror group said the attack was conducted "when American soldiers were busy searching their Afghan servants" at the gate of the base.
Camp Chapman is in Khost city, the capital of a province by the same name. It has been targeted by attacks in the past, notably one that killed seven CIA contractors and a Jordanian intelligence official in 2009.
Source: CNN | Masoud Popalzai