Epitaxial thin films and bulk crystals of the colossal
magnetoresistance (CMR) material La2/3Ca1/3MnO3 (LCMO) exhibit large discrete equilibrium resistance fluctuations in the region of phase space where the magnetoresistance effects are strongest. Strongly inhomogeneous current paths allow us to observe the random telegraph signals of individual mesoscopic regions of material fluctuating between the paramagnetic-semiconductor phase and the ferromagnetic-conductor phase. Temperature and field dependences of the Boltzmann factors of individual fluctuators yield measurements of the magnetic moment and entropy differences between these phases, and of the fluctuator volumes. These measurements provide some of the first quantitative thermodynamic information about the locally-homogeneous CMR phase transition in an otherwise strongly inhomogeneous system. Careful analysis of the field- and temperature-dependences allows us to discriminate between fluctuations across the (first-order) CMR phase boundary and fluctuations of magnetic domain orientation deep in the ferromagnetic state. Similar measurements of the closely-related CMR material La2/3Sr1/3MnO3 (LSMO) show almost no noise associated with the CMR transition, consistent with a second-order phase transition in this material.