Liquid boiling that starts,off with an insoluble gas bubble is thermodynamically analyzed. This ease is an idealization of very low gas solubility and very slow diffusion of this gas in the boiling liquid. The analysis is Made for a spherical; freely suspended bubble as well as for a bubble attached to a solid surface.: The results predict the Spontaneous formation of a stable, critical bubble at pressures higher than the saturation pressure. Stable critical radii are also predicted for pressures lower than the saturation pressure but in addition to unstable,, larger critical bubbles. These bubbles are affected by the presence and nature of a solid surface. The present analysis provides a basis for a feasible explanation of the long-debated, long-time stability of nanobubbles.