A new method is presented for measuring event-by-event fluctuations of elliptic flow (v2) using first order event planes. By studying the event-by-event distributions of v2 observables and first-order event-plane observables, average flow and event-by-event fluctuations with respect to that average can be separately determined, making appropriate allowance for the effects of finite multiplicity. The relation of flow fluctuations to eccentricity fluctuations in the initial-state participant region, as well as detector acceptance effects, are discussed.