Optical microresonators have recently attracted growing attention in the photonics community. Their applications range from quantum electrodynamics to sensors and filtering devices for optical telecommunication systems, where they will probably become an essential building block. Integration of nonlinear and electro-optical properties in resonators represents a very stimulating challenge, as it would incorporate new and more advanced functionality. Lithium niobate is an excellent candidate material, being an established choice for electro-optic and nonlinear optical applications. Here we report on the first realization of optical microring resonators in submicrometre thin films of lithium niobate. High-index-contrast films are produced by an improved crystal-ion-slicing and bonding technique using benzocyclobutene. The rings have radius Rνm, and their transmission spectrum has been tuned using the electro-optic effect. These results open new possibilities for the use of lithium niobate in chip-scale integrated optical devices and nonlinear optical microcavities.