  We show that, given integers $n_1,n_2, \ldots ,n_k$ with $2 < n_1 < n_2 <
\cdots < n_k$, there exists a local (Noetherian) unique factorization domain
that has maximal chains of prime ideals of lengths $n_1, n_2, \ldots ,n_k$
which are disjoint except at their minimal and maximal elements. In addition,
we demonstrate that unique factorization domains can have other unusual prime
ideal structures.
