  We present a survey of serendipitous extended X-ray sources and optical
cluster candidates from the Chandra Multi-wavelength Project (ChaMP). Our main
goal is to make an unbiased comparison of X-ray and optical cluster detection
methods. In 130 archival Chandra pointings covering 13 square degrees, we use a
wavelet decomposition technique to detect 55 extended sources, of which 6 are
nearby single galaxies. Our X-ray cluster catalog reaches a typical flux limit
of about ~10^-14 erg s^-1 cm^-2, with a median cluster core radius of 21
arcsec. For 56 of the 130 X-ray fields, we use the ChaMP's deep NOAO/4m MOSAIC
g, r, and i imaging to independently detect cluster candidates using a Voronoi
tessellation and percolation (VTP) method. Red-sequence filtering decreases the
galaxy fore/background contamination and provides photometric redshifts to
z~0.7. From the overlapping 6.1 square degree X-ray/optical imaging, we find
115 optical clusters (of which 11% are in the X-ray catalog) and 28 X-ray
clusters (of which 46% are in the optical VTP catalog). The median redshift of
the 13 X-ray/optical clusters is 0.41, and their median X-ray luminosity (0.5-2
keV) is L_X=(2.65\pm0.19)x10^43 ergs s^-1. The clusters in our sample that are
only detected in our optical data are poorer on average (~4sigma) than the
X-ray/optically matched clusters, which may partially explain the difference in
the detection fractions.
