We present the first speckle interferometric observations of R CrB, the prototype of a class of peculiar stars which undergo irregular declines in their visible light curves. The observations were carried out with the 6 m telescope at the Special Astrophysical Observatory near maximum light ($V=7$, 1996 Oct. 1) and at minimum light ($V=10.61$, 1999 Sep. 28). A spatial resolution of 75 mas was achieved in the K-band. The dust shell around R CrB is partially resolved, and the visibility is approximately 0.8 at a spatial frequency of 10 cycles/arcsec. The two-dimensional power spectra obtained at both epochs do not show any significant deviation from circular symmetry. The visibility function and spectral energy distribution obtained near maximum light can be simultaneously fitted with a model consisting of the central star and an optically thin dust shell with density proportional to r-2. The inner boundary of the shell is found to be 82 $R_{\star}$ (19 mas) with a temperature of 920 K. However, this simple model fails to simultaneously reproduce the visibility and spectral energy distribution obtained at minimum light. We show that this discrepancy can be attributed to thermal emission from a newly formed dust cloud.