Bismuth ferrite (BiFeO3) is a widely studied material, because of its interesting multiferroic properties. Bismuth self-limiting growth of single-phase BiFeO3 (BFO) has previously been achieved using molecular beam epitaxy (MBE), but the growth of BFO by chemical vapor deposition (CVD) has proved to be very challenging, because of the volatile nature of bismuth. The growth window regarding temperature, pressure, and precursor flow rates that will give a pure perovskite BFO phase is normally very small. In this work, we have studied the metal-organic CVD (MOCVD) growth of epitaxial BFO thin films on SrTiO3 substrates and found that by carefully controlling the amount of the iron precursor, Fe(thd)(3) (where thd = 2,2,6,6 tetra-methyl-3,5-heptanedionate), we were able to achieve bismuth self-liming growth, for the first time. The effect of the volume of the bismuth and iron precursors injected on the growth of BFO thin films is reported, and it has been found that the phase-pure films can be prepared when the Bi/Fe ratios are between 1.33 and 1.81 under temperature and pressure conditions of 650 degrees C and 10 mbar, respectively, and where the O-2 gas flow was kept constant to 1000 sccm out of a total gas flow of 3000 sccm. Piezoresponse force microscopy (PFM) studies demonstrate the presence of bipolar switching in ultrathin BFO films.