It is theoretically demonstrated that an excitable chemical system can func
tion as a spiking neuron and a chemical spiking neuron network can be const
ructed. The Oregonator is used as a model for a chemical spiking neuron. Th
e chemical spiking neuron modeled by the Oregonator is similar in behavior
to the spiking neuron model of Maass even though the Oregonator has a diffe
rent excitation mechanism from the spiking neuron model. In the spiking neu
ron network, information is encoded and processed by using the timing of th
e spikes in spiking neurons. It is shown that chemical spiking neuron netwo
rks can be constructed by the unidirectional selective coupling of the spik
ing chemical neurons. The chemical spiking neuron network can process infor
mation encoded temporally like the spiking neuron network with a restrictio
n in the range of the weight of couplings between the chemical neurons.