We obtained Ba3Yb(BO3)3 single crystals by the flux method with solutions of the BaB2O4Na2OYb2O3 system. The evolution of the cell parameters with temperature shows a slope change at temperatures near 873 K, which may indicate a phase transition that is not observed by changes appearing in the x-ray powder patterns or by differential thermal analysis (DTA). The evolution of the diffraction patterns with the temperature shows incongruent melting at temperatures higher than 1473 K. DTA indicates that there is incongruent melting and this process is irreversible. Ba3Yb(BO3)3 has a wide transparency window from 247 to 3900 nm. We recorded optical absorption and emission spectra at room and low temperature, and we determined the splitting of Yb3+ ions. We used the reciprocity method to calculate the maximum emission cross section of 0.28 10-20 cm2 at 966 nm. The calculated lifetime of Yb3+ in Ba3Yb(BO3)3 is trad = 2.62 ms, while the measured lifetime is t = 3.80 ms.