  The one-dimensional Coulomb-like potential with a real coupling constant
beta, and a centrifugal-like core of strength G = alpha^2 - {1/4}, viz. V(x) =
{alpha^2 - (1/4)}/{(x-ic)^2} + beta/|x-ic|, is discussed in the framework of
PT-symmetry. The PT-invariant exactly solvable model so formed, is found to
admit a double set of real and discrete energies, numbered by a quasi-parity q
= +/- 1.
