Abstract: Recent investigations have suggested that the six-quark combination uuddss could be a deeply bound state (S) that has eluded detection so far, and a potential dark matter candidate. We report the first search for a stable, doubly strange six-quark state in (sic) > S (Lambda) over bar(Lambda) over bar decays based on a sample of 90 x 10(6)(sic)(2S) and 110 x 10(6)(sic)(3S) decays collected by the BABAR experiment. No signal is observed, and 90% confidence level limits on the combined (sic)(2S, 3S) -> S (Lambda) over bar(Lambda) over bar branching fraction in the range (1.2-1.4) x 10(-7) are derived for m(s) < 2.05 GeV. These bounds set stringent limits on the existence of such exotic particles.