Fermi Paradox and Drake Equation
One civilisation per galaxy is pretty pessimistic. The Drake equation is a somewhat reasonable method for estimating the number of civilisations in the galaxy right now. You can certainly get the Drake equation to produce N=1, but the easiest way to do that is to assume that the average lifetime of a communicating civilisation is only a few centuries.
Two very depressing reasons for this spring to mind - either mostly civilisations destroy themselves pretty quickly, or the galaxy is very dangerous place, and everyone is hiding.