We propose to study the spin-orbit Analyzing Power, A, in p+p + p+p at large P{sub {perpendicular}}{sup 2}. We propose to run at Fermilab around Fall 1987 and scatter a high intensity unpolarized proton beam of 800 to 900 GeV from a Polarized Proton Target; we would measure the difference between the d{sigma}/dt when the target spin is up and when it is down. Our main goal is to see if the unexpected large values of A recently found at the 28 GeV AGS in proton-proton elastic scattering persist to Fermilab energies. The large A value of 24 {+-} 8% at P{sub {perpendicular}}{sup 2} = 6.5 (GeV/c){sup 2} was not only unexpected but also seems difficult to reconcile with the A = 0 prediction of conventional models of strong interactions, such as perturbative QCD. The validity of perturbative QCD is believed to improve with increasing energy and with increasing P{sub {perpendicular}}{sup 2}, and this proposed Fermilab experiment would increase the incident energy by about a factor of 30. The experiment would be done using a Polarized Proton Target (PPT) employing radiation-doped NH{sup 3} beads and a 'local' cooling power of about 130 mW at 1/2{sup o} K. Such a target …