Captive bubble experiments on surface-engineered silicon substrates with precisely tuned roughness and surface chemistry are reported. In these experiments, the substrates were submerged into water, and air bubbles were dispensed from below. Our measurements revealed a bubble-repellent behavior, with bubbles freely moving around on the submerged surfaces. Drawing an analogy to drops on superhydrophobic surfaces, this behavior is termed "superaerophobic", and the observed effects are explained with the formation of a composite wetting contact between bubble and substrate. The thermodynamics of the "superaerophobic" wetting state are analyzed, and an equation for the equilibrium contact angle is given.