We present the Brera Multi-scale Wavelet Chandra (BMW-Chandra) source catalogue drawn from essentially all Chandra ACIS-I pointed observations with an exposure time in excess of 10ks public as of March 2003 (136 observations). Using the wavelet detection algorithm developed by Lazzati et al. (1999) and Campana et al. (1999), which can characterise both point-like and extended sources, we identified 21325 sources. Among them, 16758 are serendipitous, i.e. not associated with the targets of the pointings. This makes our catalogue the largest compilation of Chandra sources to date. The 0.5-10keV absorption corrected fluxes of these sources range from 3E-16 to 9E-12 erg/cm2/s with a median of 7E-15 erg/cm2/s. The catalogue consists of count rates and relative errors in three energy bands (total, 0.5-7keV; soft, 0.5-2keV; and hard, 2-7keV), where the detection was performed, and source positions relative to the highest signal-to-noise detection among the three bands. The wavelet algorithm also provides an estimate of the extension of the source. We also extracted source counts in four additional energy bands, SB1 (0.5-1keV), SB2 (1-2keV), HB1 (2-4keV), and HB2 (4-7keV).