An Atom Trap Trace Analysis (ATTA) system based on the technique of laser manipulation of neutral atoms is being developed to count individual {sup 41}Ca atoms present in natural samples with an isotopic abundance of 10{sup -15}. Trapping of all stable calcium isotopes has been demonstrated and single-atom counting has been realized. For the most abundant isotope, {sup 40}Ca (97% isotopic abundance), a magneto-optical trap (MOT) loading rate of 2 x 10{sup 10} atoms/s has been reached at the overall capture efficiency of 1 x 10{sup -4}. System improvements could increase the efficiency by at least an order of magnitude.