  The recent solution to the fermion sign problem allows, for the first time,
the use of cluster algorithm techniques to compute certain fermionic path
integrals. To illustrate the underlying ideas behind the progress, a cluster
algorithm is constructed to study the chiral phase transition in a strongly
interacting staggered fermion model with an arbitrary mass term in 3+1
dimensions. Unlike conventional methods there is no difficulty in the cluster
method to approach the chiral (massless) limit. Results using the new algorithm
confirm that the chiral transition falls under the expected universality class.
