  In this paper we consider the zeros of the chromatic polynomial of
series-parallel graphs. Complementing a result of Sokal, showing density
outside the disk $|q-1|\leq1$, we show density of these zeros in the half plane
$\Re(q)>3/2$ and we show there exists an open region $U$ containing the
interval $(0,32/27)$ such that $U\setminus\{1\}$ does not contain zeros of the
chromatic polynomial of series-parallel graphs.
  We also disprove a conjecture of Sokal by showing that for each large enough
integer $\Delta$ there exists a series-parallel graph for which all vertices
but one have degree at most $\Delta$ and whose chromatic polynomial has a zero
with real part exceeding $\Delta$.
