  We construct from a general del Pezzo surface of degree 1 a Gorenstein stable
surfaces $X$ with $K_X^2=1$ and $p_g(X)=q(X)=0$. These surfaces are not
smoothable but give an open subset of an irreducible component of the moduli
space of stable Godeaux surfaces.
  In a particular example we also compute the canonical ring explicitly and
discuss the behaviour of pluricanonical maps.
