  We introduce an efficient scheme for the construction of quadrature rules for
bandlimited functions. While the scheme is predominantly based on well-known
facts about prolate spheroidal wave functions of order zero, it has the
asymptotic CPU time estimate $O(n log n)$ to construct an n-point quadrature
rule. Moreover, the size of the ``$n log n$'' term in the CPU time estimate is
small, so for all practical purposes the CPU time cost is proportional to $n$.
The performance of the algorithm is illustrated by several numerical examples.
