The processes leading to dust formation and the subsequent role it plays in driving mass loss in cool evolved stars is an area of intense study. Here we present high resolution ALMA Science Verification data of the continuum emission around the highly evolved oxygen-rich red supergiant VY CMa. These data enable us to study the dust in its inner circumstellar environment at a spatial resolution of 129 mas at 321 GHz and 59 mas at 658 GHz, thus allowing us to trace dust on spatial scales down to 11 R-star (71 AU). Two prominent dust components are detected and resolved. The brightest dust component. C, is located 334 mas (61 R-star) southeast of the star and has a dust mass of at least 2.5 x 10(-4) M-circle dot. It has a dust emissivity spectral index of beta = -0.1 at its peak, implying that it is optically thick at these frequencies with a cool core of T-d less than or similar to 100 K. Interestingly, not a single molecule in the ALMA data has emission close to the peak of this massive dust clump. The other main dust component. VY, is located at the position of the star and contains a total dust mass of 4.0 x 10(-)5 M-circle dot. It also contains a weaker dust feature extending over 60 R-star to the north with the total component having a typical dust emissivity spectral index of beta = 0.7. We find that at least 17% of the dust mass around VY CMa is located in clumps ejected within a more quiescent roughly spherical stellar wind, with a quiescent dust mass loss rate of 5 x 10(-6) M-circle dot yr(-1). The anisotropic morphology of the dust indicates a continuous, directed mass loss over a few decades, suggesting that this mass loss cannot be driven by large convection cells alone.