Deal k cards uniformly at random

You have $n$ distinct items and want a hand of $k$ of them ($k \le n$), drawn uniformly: every possible $k$-item outcome equally likely.

Return $k$ items so that all $\binom{n}{k}$ subsets are equally likely, using only a uniform random integer generator. Do the work in $O(k)$ swaps, not $O(n)$.