The expected performance of hashing with chaining in the prime area is analyzed. The basic idea of this overflow handling technique is straightforward: a record that does not fit into its home bucket, is placed in some other (non-full) bucket and connected to an overflow chain emanating from the home bucket. The variant studied can be characterized as follows: each bucket has several, noncoalescing overflow chains, empty space is located by a random search, and records are not relocated after insertion. The analysis is asymptotic and it is assumed that there are no deletions. Simple closed formulas cannot be obtained, except in the case of bucket size one, but numerical results are readily computed. The expected performance compares favourably with that of other overflow techniques. This also holds for large pages, provided that several overflow chains per page are used.