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.