Summary: Let \(S_n\), \(n\geq 1\), be a random walk on a polynomial hypergroup \((\mathbb{N}_0,*)\), that is, a Markov chain on the nonnegative integers with stationary transition probabilities \(P_{ij} = \delta_i*\mu (\{j\})\), where \(\mu\) is a fixed probability measure on \(\mathbb{N}_0\). Under certain conditions on this measure, the principle of large deviations is shown for the distributions of \(S_n/n\). This result comprises the large deviation principle for birth and death random walks associated with the polynomials generating the polynomial hypergroup.