An example of a higher spin gravity in four-dimensional flat space has recently been constructed by D. Ponomarev and E. D. Skvortsov, J. Phys. A, 50, 095401(2017). This theory is chiral and the action is written in the light-cone gauge. The theory has certain stringy features, e.g., admits Chan-Paton factors. We show that the theory is consistent, both at the classical and quantum level. Even though the interactions are nontrivial, due to the coupling conspiracy all tree level amplitudes vanish on shell. The loop corrections also vanish. Therefore, the full quantum S matrix is one and the theory is consistent with the numerous no-go theorems. This provides the first example of a (quantum) interacting higher spin gravity with an action. We argue that higher spin gravities in anti-de Sitter space should display the same features.