  We study the predictions of the simplest SU(5) grand unified model within the
framework of minimal supergravity, including constraints from the radiative
breaking of electroweak symmetry. As a consequence of the unification of the
$b$-quark and $\tau$-lepton Yukawa couplings, the top quark mass is predicted
to be close to its fixed point value. We delineate the regions of the
supergravity parameter space allowed by constraints from the non-observation of
proton decay and from the requirement that the LSP does not overclose the
universe. These constraints lead to a definite pattern of sparticle masses: the
feature unique to Yukawa unified models is that some of the third generation
squarks are much lighter than those of the first two generations. Despite the
fact that all sparticle masses and mixings are determined by just four SUSY
parameters at the GUT scale (in addition to $m_t$), we find that the signals
for sparticle production can vary substantially over the allowed parameter
space. We identify six representative scenarios and study the signals from
sparticle production at the LHC. We find that by studying the signal in various
channels, these scenarios may be distinguished from one another, and also from
usually studied ``minimal models'' where squarks and sleptons are taken to be
degenerate. In particular, our studies allow us to infer that some third
generation squarks are lighter than other squarks---a feature that could
provide the first direct evidence of supergravity grand unification.
