Abstract: We design and analyze an unfitted hybrid high-order (HHO) method for the acoustic wave equation. The wave propagates in a domain where a curved interface separates subdomains with different material properties. The key feature of the space discretization method is that the interface can cut more or less arbitrarily through the mesh cells. We address both the second-order formulation in time of the wave equation and its reformulation as a first-order system. For explicit time-stepping schemes, we study the CFL condition and observe that the unfitted approach combined with local cell agglomeration leads to a comparable condition as when using fitted meshes.