The Chandra Multiwavelength Project (ChaMP) is a wide-area (~14 deg2) survey of serendipitous Chandra X-ray sources, aiming to establish fair statistical samples covering a wide range of characteristics (such as absorbed active galactic nuclei, high-z clusters of galaxies) at flux levels (fX ~ 10-15 to 10-14 ergs s-1 cm-2) intermediate between the Chandra deep surveys and previous missions. We present the first ChaMP catalog, which consists of 991 near on-axis, bright X-ray sources obtained from the initial sample of 62 observations. The data have been uniformly reduced and analyzed with techniques specifically developed for the ChaMP and then validated by visual examination. To assess source reliability and positional uncertainty, we perform a series of simulations and also use Chandra data to complement the simulation study. The false source detection rate is found to be as good as or better than expected for a given limiting threshold. On the other hand, the chance of missing a real source is rather complex, depending on the source counts, off-axis distance (or PSF), and background rate. The positional error (95% confidence level) is usually less than 1'' for a bright source, regardless of its off-axis distance, while it can be as large as 4'' for a weak source (~20 counts) at a large off-axis distance (Doff-axis > 8'). We have also developed new methods to find spatially extended or temporary variable sources, and those sources are listed in the catalog.