Using a sample of 158 x 10(6) Y(2S) events collected with the Belle detector, we search for the first time for double-charmonium decays of the P-wave spin-triplet bottomonium states (Y(2S) -> gamma chi(bJ), chi(bJ) -> J/psi J/psi, J/psi psi', psi'psi' for J 0, 1, and 2). No significant chi(bJ) signal is observed in the double-charmonium mass spectra, and we obtain the following upper limits: B(chi(bJ) -> J/psi J/psi) J/psi psi') psi'psi') < 3.1 x 10(-5), 6.2 x 10(-5), 1.6 x 10(-5) for J = 0, 1, and 2, respectively, at the 90% confidence level.
These limits are significantly lower than the central values (with uncertainties of 50% to 70%) predicted using the light cone formalism but are consistent with calculations using the nonrelativistic QCD (NRQCD) factorization approach.