This paper deals with Schauder type estimates for a class of degenerate elliptic operators \(\mathcal A\) and parabolic operators \(u_t-{\mathcal A}u\) with unbounded coefficients in \(\mathbb{R}^n\). In the elliptic case the operators \(\mathcal A\) form a subclass of the hypoelliptic second-order operators in the sense of Hörmander. The author defines a suitable distance \(d\) in \(\mathbb{R}^n\) and a Hölder type space \(C^\theta_d\) with an exponent \(\theta\), \(0<\theta<1\), with respect to \(d\). It is proved that, if \(\lambda>0\), then for each function \(f\in C^\theta_d(\mathbb{R}^n)\) there exists a unique solution \(u\) of the equation \(\lambda u-{\mathcal A}u= f\) in the space of uniformly continuous and bounded functions. Moreover, \(u\in C^{2+\theta}_d\) and the following a priori estimate holds: \(|u|_{C^{2+\theta}_d}\leq C|f|_{C^\theta_d}\).