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In this paper we consider the zeros of the chromatic polynomial ofseries-parallel graphs. Complementing a result of Sokal, showing densityoutside 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 theinterval $(0,32/27)$ such that $U\setminus\{1\}$ does not contain zeros of thechromatic polynomial of series-parallel graphs.  We also disprove a conjecture of Sokal by showing that for each large enoughinteger $\Delta$ there exists a series-parallel graph for which all verticesbut one have degree at most $\Delta$ and whose chromatic polynomial has a zerowith real part exceeding $\Delta$.

On the location of chromatic zeros of series-parallel graphs