Fatigue resistance is a key property of the service lifetime of structural materials. Carbon nanotubes (CNTs) are one of the strongest materials ever discovered, but measuring their fatigue resistance is a challenge because of their size and the lack of effective measurement methods for such small samples. We developed a noncontact acoustic resonance test system for investigating the fatigue behavior of centimeter-long individual CNTs. We found that CNTs have excellent fatigue resistance, which is dependent on temperature, and that the time to fatigue fracture of CNTs is dominated by the time to creation of the first defect.