Quasi-particles (QPs) are excitations of the superconducting state. The behavior of QPs in Bi2Sr2CaCu2O8 in a magnetic field was probed by measurement of the thermal conductivity kappa. An anomaly in kappa was observed at low temperatures, At a transition field H-k, kappa displayed a sharp break in slope, followed by a plateau region in which it ceased to change with increasing field. The nonanalytic nature of the break at H-k suggests a phase transition of the condensate to a state in which the QP current is zero (the system remains superconducting). Detailed measurements of the new regime are presented, and implications for the QPs and the superconducting state are discussed.