Jets produced in high transverse energy proton-nucleus collisions at 400 GeV/c were recorded in a calorimeter study at Fermilab. The jets were identified with two different jet-finding algorithms; the results from the two algorithms agree. For the eight nuclear targets with atomic number, A, ranging from 1 to 207 (H\sb2, He, Be, C, Al, Cu, Sn and Pb), the cross section increases as A\sp1.35±0.01 over mean jet pair transverse momentum of 4 to 8 GeV/c. The enhancement, however, depends on the class of jets selected; for example the cross section increases as A\sp1 for highly planar high-transverse-momentum jet events and as A\sp1.65 for non-planar high-transverse-momentum events. Jet properties were studied as a function of jet transverse momentum and A. In general as A increases, the number of particles in the jets increases while their collimation and coplanarity decrease. Also with increasing A, the proton transfers more of its energy into the target fragmentation region instead of the forward or central regions. Multiple scattering models describe nuclear enhancement, however fits to our data require negative coefficients in the higher order terms of the expansion, presenting a challenge to simple multiple scattering models.