  Let a sequence $(P_n)$ of polynomials in one complex variable satisfy a
recurre ce relation with length growing slowlier than linearly. It is shown
that $(P_n) $ is an orthonormal basis in $L^2_{\mu}$ for some measure $\mu$ on
$\C$, if and o ly if the recurrence is a $3-$term relation with special
coefficients. The supp rt of $\mu$ lies on a straight line. This result is
achieved by the analysis of a formally normal irreducible Hessenberg operator
with only finitely many nonzero entries in every row. It generalizes the
classical Favard's Theorem and the Representation Theorem.
