Given a stream $\mathcal{S}$ of insertions and deletions of edges of an underlying graph $G$ (with fixed vertex set $V$ where $n=|V|$ is the number of vertices of $G$), we propose a dynamic algorithm that maintains a maximal independent set (MIS) of $G$ (at any time $t$ of the stream $\mathcal{S}$) with amortized update time $O(\log^3 n)$.