The dynamics of a chemical reaction network (CRN) is often modeled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of concentrations of chemical species involved. Given an arbitrarily large integer\documentclass[12pt]{minimal}
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				\begin{document}$$K \in {\mathbb N}$$\end{document}K∈N, we show that there exists a CRN such that its ODE model has at leastKstable limit cycles. Such a CRN can be constructed with reactions of at most second-order provided that the number of chemical species grows linearly withK. Bounds on the minimal number of chemical species and the minimal number of chemical reactions are presented for CRNs withKstable limit cycles and at most second order or seventh-order kinetics. We also show that CRNs with only two chemical species can haveKstable limit cycles, when the order of chemical reactions grows linearly withK.