We report a measurement of the longitudinal double-spin asymmetry A(LL) and the differential cross section for inclusive midrapidity jet production in polarized proton collisions at square root of s = 200 GeV. The cross section data cover transverse momenta 5pT50 GeV/c and agree with next-to-leading order perturbative QCD evaluations. The A(LL) data cover 5pT17 GeV/c and disfavor at 98% C.L. maximal positive gluon polarization in the polarized nucleon.