We report the first long-baseline interferometric observations of R CrB. The observations were carried out at the Infrared Optical Telescope Array (IOTA), using our new JHK beam combiner which enables us to record fringes simultaneously in the J-, H-, and K-bands. The circumstellar envelope of R CrB is resolved at a baseline of 21 m, and the K-band visibility is derived to be 0.61 ± 0.03 along a position angle of about 170 degrees. The visibility obtained with IOTA, as well as speckle visibilities with baselines up to 6 m and the spectral energy distribution (SED), are fitted with 2-component models consisting of the central star and an optically thin dust shell. The K-band visibilities predicted by the models are about 10% smaller than the visibility obtained with IOTA. However, given the simplifications adopted in our models and the complex nature of the object, this can be regarded as rough agreement. As a hypothesis to explain the small discrepancy, we propose that there might be a group of newly formed dust clouds, which might appear as a third visibility component.