The chemotaxis-diffusion growth system in a rectangular domain is studied. We study the system from a point of view of pattern formation phenomena. The linear analysis tells us that a trivial solution (spatially uniform solution) is destabilized if the chemotaxis coefficient is large. And it is possible to choice a set of parameters such that three modes which compose a hexagonal pattern are destabilized simultaneously. Around this critical point, we analyze the chemotaxis system based on the center manifold theory. As a result, the normal form on the center manifold is obtained. Using the normal form, we discuss the existence and stabilities of a regular hexagonal pattern in the chemotaxis system.