We search for invisible decays of the Upsilon(1S) meson using a sample of 91.4 x 10^{6} Upsilon(3S) mesons collected at the BaBar/PEP-II B-factory. We select events containing the decay Upsilon(3S) -> pi+ pi- Upsilon(1S) and search for evidence of an undetectable Upsilon(1S) decay recoiling against the dipion system. We set an upper limit on the branching fraction BR(Upsilon(1S) -> invisible) < 3.0 x 10^{-4} at the 90% confidence level.