In the transfer matrix framework of electromagnetic transport, we calculate the group velocities in a one-dimensional photonic crystal composed of a biaxially anisotropic chiral material and dielectric material. According to the isofrequency curves, it is unravelled that two polarized waves possess negative group velocities. As a result, negative refraction can be achieved in the present configuration. In addition, the chirality has a significant influence on the group velocities in the biaxially anisotropic chiral photonic crystal, which even causes the group velocities to change from positive to negative. Our investigations may have potential applications in the chiral-based negative refraction devices.