This paper presents a fully adaptive fault location algorithm for three-terminal lines based on synchronized phasor measurements obtained by Phasor Measurement Units (PMUs). The proposed algorithm utilizes only PMU synchronized measurements and does not require any data to be provided by the electric utility. Line parameters for each section of the line and Thevenin's equivalents (TEs) of the system at each of the three terminals are determined online, utilizing three independent sets of pre-fault PMU measurements. This ensures that the actual operating conditions of the system are adequately considered. Fault-location accuracy evaluation of the proposed algorithm is performed with respect to various factors such as fault position and fault type. The proposed algorithm is simulated using both PSCAD/EMTDC and MATLAB and tested on a 500 kV system. Simulation results reveal that the developed algorithm is capable of producing reliable and very accurate solutions.