We present the first stringent tests of a novel calibration system based on a laser frequency comb (LFC) for radial velocity measurements. The tests were obtained with the high-resolution, optical spectrograph, High Accuracy Radial velocity Planet Searcher. By using only one echelle order, we obtain a calibration repeatability of 15cms-1 for exposures that are several hours apart. This is comparable with a simultaneous calibration using a Th-Ar lamp that makes use of all 72 echelle orders. In both cases, the residuals are compatible with the computed photon noise. Averaging all LFC exposures, recorded over a few hours, we could obtain a calibration curve with residuals of 2.4ms-1. Thanks to the adjustable and optimally chosen line density of the LFC, we resolve a periodicity of 512 pixels in the calibration curve that is due to the manufacturing process of the CCD mask. Previous Th-Ar calibration was unable to resolve these systematic deviations, resulting in a deviation of up to 70ms-1 from the true calibration curve. In future, we hope to be able to make use of all echelle orders in order to obtain a calibration repeatability below 1cms-1 and absolute calibration within a few ms-1.