We have demonstrated the first fully stabilized frequency comb generated by an ultrafast Er:Vb:glass laser. The SESAM-modelocked, diode-pumped laser uses a high-Q cavity which results in low-noise operation. A coherent, octave-spanning SC is generated by nonlinear spectral broadening in a polarization maintaining highlynonlinear fiber. We observe a more than 10-times improvement in the free-running CEO frequency linewidth compared to free-running femtosecond fiber laser systems operating in this spectral region. The CEO frequency and the repetition rate are stabilized to the same 10-MHz external reference over hours. The Allan deviation of the 20-MHz CEO reaches 10 -8 at 1-s with an H-maser as an external reference and a stable locked operation of more than 11 hours was achieved in a preliminary long-term evaluation. A CEO-beat signal can still be observed at a large reduction of the pump power, resulting in a reduced intracavity pulse energy and in an increased pulse duration up to 260 fs. We expect that this result will have a significant impact for the future development of more compact stable frequency combs as the relatively long pulse duration relaxes the requirements on the modelocked laser. This will become even more important for gigahertz pulse repetition rates.