Chemically active Brownian particles with surface catalytic reactions may repel each other due to diffusiophoretic interactions in the reaction and product concentration fields. The system behavior can be described by a ‘‘chemical’’ coupling parameter $\Gamma_c$ that compares the strength of diffusiophoretic repulsion to Brownian motion, and by a mapping to the classical electrostatic one component plasma (OCP) system. When confined to a constant-volume domain, body-centered cubic (bcc) crystals spontaneously form from random initial configurations when the repulsion is strong enough to overcome Brownian motion. Face-centered cubic (fcc) crystals may also be stable. The ‘‘melting point’’ of the ‘‘liquid-to-crystal transition’’ occurs at $\Gamma_c\approx 140$ for both bcc and fcc lattices.