  We describe a simple algorithm for sampling $n$-qubit Clifford operators
uniformly at random. The algorithm outputs the Clifford operators in the form
of quantum circuits with at most $5n + 2n^2$ elementary gates and a maximum
depth of $\mathcal{O}(n\log n)$ on fully connected topologies. The circuit can
be output in a streaming fashion as the algorithm proceeds, and different parts
of the circuit can be generated in parallel. The algorithm has an
$\mathcal{O}(n^2)$ time complexity, which matches the current state of the art.
The main advantage of the proposed algorithm, however, lies in its simplicity
and elementary derivation.
