Single crystals of Na-doped Ca2CuO2Cl2 have been grown for the first time by a flux method under high pressures of up to 5.5 GPa. By changing the Na-solubility limit through the applied pressure, the Na content x was successfully controlled without introducing appreciable compositional inhomogeneity within the millimeter-sized crystals. Structural and chemical characterization indicated that the crystals span the phase diagram continuously from the parent antiferromagnetic insulator to an underdoped high-temperature superconductor. Because of the well-defined cleavage plane and resulting high surface quality, these oxychloride single crystals will provide a unique opportunity to explore the electronic evolution of the high-temperature superconductors, using spectroscopic techniques such as scanning tunneling microscopy/spectroscopy and angle-resolved photoemission spectroscopy.