We consider the hash function (h(x) = ((ax+b) \bmod p) \bmod n) where (a,b) are chosen uniformly at random from (\{0,1,\ldots,p-1\}). We prove that when we use (h(x)) in hashing with chaining to insert (n) elements into a table of size (n) the expected length of the longest chain is (\tilde{O}!\left(n^{1/3}\right)). The proof also generalises to give the same bound when we use the multiply-shift hash function by Dietzfelbinger et al. [Journal of Algorithms 1997].