A 4:1 mixture of CH4 and BrCl diluted in He are coexpanded into a vacuum chamber and the reaction of methane with atomic chlorine is initiated by photolysis of BrCl. Near 420 nm, the resulting mixture of ground- and excited-state chlorine atoms have spatial anisotropies of beta (phot)=-0.7 for the Cl(P-2(3/2))+Br channel and beta (phot)=+1.8 for the Cl-*(P-2(1/2))+Br channel. The speed-dependent spatial anisotropy beta (rxn)(nu) of the CH3(nu =0) reaction product is detected by 2+1 resonance-enhanced multiphoton ionization. Our results indicate that the Cl*+CH4 reaction is unimportant in the near-threshold collision energy range of 0.13-0.16 eV, whereas the reaction with ground-state Cl atoms with CH4 excited with one quantum in the nu (2) (torsion) or nu (4) (bending) mode is dominant.