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: {\it
i}). first and second generation scalars in the multi-TeV range, {\it ii}).
third generation scalars, \mu and m_A in the few-TeV range and {\it iii}).
gluinos in the \sim 350-500 GeV range with chargino masses around 100-160 GeV.
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 W1Z2-> 3\ell channel, and should exhibit the same dilepton
mass edge as in the gluino cascade decay signal.Comment: 25 pages including 18 EPS figure