Solution of a plane frictionless contact problem for two rough elastic solids is considered. An exact solution of the problem resulting in a singly connected contact region is considered, and it is conveniently expressed in the form of a series in Chebyshev polynomials. A sufficient (not necessary) condition for a contact of the solids to be singly connected is derived. The singly connected contact condition depends on the surface micro-topography, material effective elastic modulus, solid shapes, and applied load. It is determined that under certain conditions, a normal contact of three times differentiable rough surfaces with sufficiently small asperity amplitude and/or sufficiently large applied load is singly connected.