We report for the first time that transmission of optical pulses centered at a wavelength of 1550 nm through a tapered dual-core As2Se3-PMMA fiber inscribes an antisymmetric long-period grating. The pulse power is equally divided between even and odd modes that superpose along the dual-core fiber to form an antisymmetric intensity distribution. A permanent refractive-index change that matches the antisymmetric intensity distribution is inscribed due to photosensitivity at the pulse central wavelength. The evolution of the transmission spectrum of the dual-core fiber is experimentally measured as the accumulated time that the fiber is exposed to the pulse is increased. A theoretical model of an antisymmetric long-period grating in a dual-core fiber computationally reproduces the experimentally observed evolution of the transmission spectrum. Experimental results indicate that antisymmetric long-period gratings induce effective group-velocity matching between the even and odd modes of the dual-core fiber, and reveal for the first time that long-period gratings can lead to slow light propagation velocities.