We have applied the experimental technique of core extraction [W, R, Simpson et al., J. Chem. Phys, 103, 7299 (1995)] combined with resonance-enhanced multiphoton ionization (REMPI) with a polarized laser beam to probe the angular-momentum alignment of the HCl product of the reaction of Cl with vibrationally excited CH4(v(3)=1). The core extraction method permits us to distinguish products scattered in different directions in the center-of-mass frame, and thus we are able to determine the rotational alignment for various product scattering angles for individual KCl(v’,J’) quantum states (a state-resolved three-vector correlation), For the forward-scattered HCl(v’=1, J’=1) we observe a large positive rotational alignment. This positive velocity-angular-momentum correlation is interpreted to be the result of the angular momentum of the HCl product being directed in the plane perpendicular to the line-of-centers force in a simple hard-sphere scattering model.