  Raynaud has shown that over a general curve of genus $g \ge 2$, every
semistable bundle of rank three and integral slope admits a theta divisor. We
show that this can fail for special curves: Over any bielliptic curve of genus
$g \ge 5$, we construct a stable rank three bundle of trivial determinant with
no theta divisor. This gives a partial answer to a question of Beauville.
