Using the data sample of 711 fb(-1) of Upsilon(4S) on-resonance data taken by the Belle detector at the KEKB asymmetric-energy electron-positron collider, we present the first measurements of branching fractions of the decays B- -> (Lambda) over bar (-)(c)Xi'(0)(c), B- -> (Lambda) over bar (-)(c)Xi(c)(2645)(0), and B- -> (Lambda) over bar (-)(c)Xi(c)(2790)(0). The signal yields for these decays are extracted from the recoil mass spectrum of the system recoiling against (Lambda) over bar (-)(c) baryons in selected B- candidates. The branching fraction of B- -> (Lambda) over bar (-)(c)Xi(c)(2790)(0) is measured to be (1.1 +/- 0.4 +/- 0.2) x 10(-3), where the first uncertainty is statistical and the second is systematic. The 90% credibility level upper limits on B(B- -> (Lambda) over bar (-)(c)Xi'(0)(c)) and B(B- -> (Lambda) over bar (-)(c)Xi(c)(2645)(0)) are determined to be 6.5 x 10(-4) and 7.9 x 10(-4), respectively.