Through the use of laser-induced fluorescence spectroscopy, product rotational population distributions were recorded for the Ba (1S0) + HI(X(1)SIGMA+) --> BaI(X(2)SIGMA+, nu = O) + H(2S1/2) reaction under well-defined, crossed-beam conditions. In this kinematically constrained reaction, orbital angular momentum of the reagents L(reag) is channeled almost exclusively into rotational angular momentum of the products J(prod). Consequently, \J(prod)\ congruent-to-mu-nu(rel)b, where mu is the reduced mass of the reactants, nu(rel) is their relative velocity, and b is the impact parameter of the reactive collision. For relative velocity distributions with mean values ranging from 860 to 1000 m s-1, the BaI nu = 0 rotational distributions were found to peak sharply at high J values (greater-than-or-similar-to 420). Nonlinear least-squares analysis showed the specific opacity function (impact parameter distribution) for the formation of vibrationless BaI product to be exceptionally narrow (approximately 0.3 angstrom FWHM) with a pronounced maximum at the highest energetically allowed impact parameter approximately 4.5 angstrom.