Abstract Stellar oscillations can be of topological origin. We reveal this deep and so far hidden property of stars by establishing a novel parallel between stars and topological insulators. We construct an Hermitian problem to derive the expression of the stellar acoustic–buoyant frequency S of nonradial adiabatic pulsations. A topological analysis then connects the changes of sign of the acoustic – buoyant frequency to the existence of Lamb-like waves within the star. These topological modes cross the frequency gap and behave as gravity modes at low harmonic degree ℓ and as pressure modes at high ℓ. S is found to change sign at least once in the bulk of most stellar objects, making topological modes ubiquitous across the Hertzsprung–Russell diagram. Some topological modes are also expected to be trapped in regions where the internal structure varies strongly locally.