The properties of the coupling between chemical oscillators were studied in the discrete chemical oscillation system which was realized by immersing cation exchange beads loaded with ferroin in the Belousov-Zabotinskii reaction solution. A phase diagram of coupling states was obtained as a function of natural frequencies of oscillators and the distance d between oscillators. The synchronization was found not to be attributed to a simple entrainment of the slower oscillator by the faster one. Various entrainments between oscillators occurred depending on ratios of natural frequencies in the uncoupled state. A chaotic behavior was found at the boundary between stably coupled regions with frequency ratios of n/1 where n is an integer. Furthermore, effects of external perturbation on the coupling were investigated. Irregular oscillations were induced by illumination with a He-Ne laser light, which strongly depended on the phase of oscillator at the beginning of illumination. Such irregular behaviors were localized within the illuminated bead. This indicates that two oscillators are decoupled by illumination.