Single crystals of the compound LaFePO were prepared using a flux growth technique at high temperatures. Electrical resistivity measurements reveal metallic behavior and a resistive transition to the superconducting state at a critical temperature T_c ~ 6.6 K. Magnetization measurements also show the onset of superconductivity near 6 K. In contrast, specific heat measurements manifest no discontinuity at T_c. These results lend support to the conclusion that the superconductivity is associated with oxygen vacancies that alter the carrier concentration in a small fraction of the sample, although superconductivity characterized by an unusually small gap value can not be ruled-out. Under applied magnetic fields, T_c is suppressed anisotropically for fields perpendicular and parallel to the ab-plane, suggesting that the crystalline anisotropy strongly influences the superconducting state. Preliminary high-pressure measurements show that T_c passes through a maximum of nearly 14 K at ~ 110 kbar, demonstrating that significantly higher T_c values may be achieved in the phosphorus-based oxypnictides.