The polarizability of a two-dimensional interacting electron gas is calculated in various limits. First, we obtain the temperature dependence of the non-interacting polarizability π0(q, ω). Next, we calculate the first-order (exchange correction π1(q) to the static polarizability. The relevance of this result to possible charge density wave instabilities is discussed and the connection with the work of Kelly and Falicov is established. © 1978.