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 $τ$-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.

28 pages Revtex files with 5 PS figures available from drees@phenom.physics.wisc.edu, Preprint nos. FSU-HEP-940311, KEK-TH-392, MAD/PH/825, UH-511-785-94