This paper considers Cell-Free Massive Multiple Input Multiple Output (MIMO) systems with the assistance of an RIS for enhancing the system performance. Distributed maximum-ratio combining (MRC) is considered at the access points (APs). We introduce an aggregated channel estimation method that provides sufficient information for data processing. The considered system is studied by using asymptotic analysis which lets the number of APs and/or the number of RIS elements grow large. A lower bound for the channel capacity is obtained for a finite number of APs and engineered scattering elements of the RIS, and closed-form expression for the uplink ergodic net throughput is formulated. In addition, a simple scheme for controlling the configuration of the RIS scattering elements is proposed. Numerical results verify the effectiveness of the proposed system design and the benefits of using RISs in Cell-Free Massive MIMO systems are quantified.