Stable nonsupersymmetric anti-de Sitter (AdS) vacua of string theory are widely believed not to exist. In this Letter, we analytically compute the full bosonic Kaluza-Klein spectrum around the G_{2}-invariant nonsupersymmetric AdS_{4} solution of massive IIA supergravity and show that it is perturbatively stable. We also provide evidence that six other nonsupersymmetric AdS_{4} solutions of massive IIA supergravity are perturbatively stable. Since previous studies have indicated that these AdS vacua may also be nonperturbatively stable, our findings pose a challenge to the swampland conjecture.