We present a novel system where an optical cavity is integrated with a microfabricated planar-electrode ion trap. The trap electrodes produce a tunable periodic potential allowing the trapping of up to 50 separate ion chains aligned with the cavity and spaced by 160 μm in a one-dimensional array along the cavity axis. Each chain can contain up to 20 individually addressable Yb+ ions coupled to the cavity mode. We demonstrate deterministic distribution of ions between the sites of the electrostatic periodic potential and control of the ion–cavity coupling. The measured strength of this coupling should allow access to the strong collective coupling regime with≲ 10 ions. The optical cavity could serve as a quantum information bus between ions or be used to generate a strong wavelength-scale periodic optical potential.