In this paper, we study the cell probe complexity of evaluating an $n$-degree polynomial $P$ over a finite field $F$ of size at least $n^{1+Omega(1)}$. More specifically, we show that any static data structure for evaluating $P(x)$, where $x in F$, must use $Omega(lg |F|/lg(Sw/nlg|F|))$ cell probes to answer a query, where $S$ denotes the space of the data structure in number of cells and $w$ the cell size in bits. This bound holds in expectation for randomized data structures with any constant error probability $delta