The requirement of t-b-tau Yukawa coupling unification is common in simple grand unified models based on the gauge group SO( 10), and it also places a severe constraint on the expected spectrum of superpartners. For Yukawa-unified models with mu > 0, the spectrum is characterized by three mass scales: i). first and second generation scalars in the multi-TeV range, ii). third generation scalars, mu and m(A) in the few-TeV range and iii). gluinos in the similar to 350 - 500GeV range with chargino masses around 100 - 160GeV. In such a scenario, gluino pair production should occur at large rates at the CERN LHC, followed by gluino three-body decays into neutralinos or charginos. Discovery of Yukawa-unified SUSY at the LHC should hence be possible with only 1 fb(-1) of integrated luminosity, by tagging multi-jet events with 2-3 isolated leptons, without relying on missing E-T. A characteristic dilepton mass edge should easily be apparent above Standard Model background. Combining dileptons with b-jets, along with the gluino pair production cross section information, should allow for gluino and neutralino mass reconstruction. A secondary corroborative signal should be visible at higher integrated luminosity in the (chi) over tilde (+/-)(1)(chi) over tilde (0)(2) --> 3l channel, and should exhibit the same dilepton mass edge as in the gluino cascade decay signal.