A massive naked singularity would be cloaked by accreted matter, and thus may appear to a distant observer as an opaque (quasi-)spherical surface of a fluid, not unlike that of a star or planet. We present here analytical solutions for levitating atmospheres around a wide class of spherically symmetric naked singularities. Such an atmosphere can be constructed in every space-time which possesses a zero-gravity radius and which is a solution of a (modified-)gravity theory possessing the usual conservation laws for matter. Its density peaks at the zero-gravity radius and the atmospheric fluid is supported against infall onto the singularity by gravity alone. In an astrophysical context, an opaque atmosphere would be formed in a very short time by accretion of ambient matter onto the singularity - in a millisecond for an X-ray binary, in a thousand seconds for a singularity traversing interstellar space, and a thousand years for a singularity that is the central engine of an AGN.