The conventional design of cellular systems prescribes the separation of uplink and downlink transmissions via time-division or frequency-division duplex. Recent advances in analog and digital domain self-interference interference cancellation challenge the need for this arrangement and open up the possibility to operate base stations, especially low-power ones, in a full-duplex mode. As a means to cope with the resulting downlink-to-uplink interference among base stations, this letter investigates the impact of the Cloud Radio Access Network (C-RAN) architecture. The analysis follows an information theoretic approach based on the classical Wyner model. The analytical results herein confirm the significant potential advantages of the C-RAN architecture in the presence of full-duplex base stations, as long as sufficient fronthaul capacity is available and appropriate mobile station scheduling, or successive interference cancellation at the mobile stations, is implemented.