A four-stage, Tm-doped fiber amplifier chain emitted 608 W of single-frequency (SF) output power with 53 dB gain, 54% slope efficiency, and M2 = 1.05 beam quality. The output power was limited by available pump power. The final amplifier stage preserved the input <5-MHz linewidth and imposed negligible phase noise above 3 kHz. SBS limits at the 2040-nm operating wavelength were measured by splicing different lengths of passive fiber to the amplifier exit. Thermal limits of the fiber were explored analytically and are consistent with the measured power performance. Comparison of the SBS and thermal limits suggests a maximum SF power of ~750 W from this fiber configuration, with further potential to scale past 1 kW with different fiber parameters. To our knowledge, this is the highest power reported to date from any single-frequency, single-mode fiber laser.© (2009) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.