Ranging ambiguity is the major challenge in most LiDAR techniques with amplitude modulation, which limits the performance of range detection due to the tradeoff between the ranging precision and the unambiguous range. Here we propose a novel disambiguation method using a laser with chirped amplitude modulation (sweeping modulation frequency), which can in theory infinitely expand the unambiguous range and completely solve the ranging ambiguation problem. The usage of the earlier proposed Chirped Amplitude-Modulated Phase-Shift (CAMPS) technique enables us to detect the phase-shift of chirped signals with high precision. Incorporating this technique with the proposed disambiguation method, the absolute distance well beyond the conventional unambiguous range can easily be found with merely <1% frequency sweep range. When certain conditions are met, the Non-Mechanical Spectrally Scanned LiDAR (NMSL) system employing the CAMPS method and the Dispersion-Tuned Swept Laser (DTSL) can also realize disambiguation in non-mechanical line-scanning measurement.