We describe a previously unobserved phase transition in the plastic flow regime of the highly anisotropic superconductor HgBa₂CuO_{4 + δ}. This phase transition is marked by a sudden change in the glassy exponent. It is also marked by a change in the behavior of the plastic flow barrier U* as a function of temperature. Before the phase transition, U* decreases linearly with increasing temperature. After the phase transition, there is no clear relationship between U* and temperature. So far, we have been unable to explain this phase transition in terms of any existing theoretical modelss for the plastic flow barrier. In the future, we intend to look for possible causes of this phase transition in the microscopic forces acting on each vortex, independent of previous results on the plastic flow barrier.