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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 Υ → S Λ Λ decays based on a sample of 90 × 10 6 Υ (2S) and 110 × 10 6 Υ (3S) decays collected by the BABAR experiment. No signal is observed, and 90% confidence level limits on the combined Υ (2S, 3S) → S Λ Λ branching fraction in the range (1.2 − 1.4) × 10 −7 are derived for mS < 2.05 GeV. These bounds set stringent limits on the existence of such exotic particles.