A thermodynamic analysis of the size, shape, and stability of nanobubbles is carried out by modifying classical nucleation theory to include the supersaturation dependence of the surface tension. It is shown that the free energy of a nanobubble is a minimum at the critical radius when the contact line is pinned, that the size of the nanobubble is determined by the decrease in the surface tension caused by the degree of supersaturation, and that together these explain the increased exterior contact angle of a nanobubble compared with the corresponding angle of a macroscopic bubble or droplet on the same surface.