A frequency comb generated by a 167 MHz repetition frequency erbium-doped fiber ring laser using a carbon nanotube saturable absorber is phase-stabilized for the first time. Measurements of the in-loop phase noise show an integrated phase error on the carrier envelope offset frequency of 0.35 radians. The carbon nanotube fiber laser comb is compared with a CW laser near 1533 nm stabilized to the nu(1) + nu(3) overtone transition in an acetylene-filled kagome photonic crystal fiber reference, while the CW laser is simultaneously compared to another frequency comb based on a Cr:Forsterite laser. These measurements demonstrate that the stability of a GPS-disciplined Rb clock is transferred to the comb, resulting in an upper limit on the locked comb's frequency instability of 1.2 x 10(-11) in 1 s, and a relative instability of <3 x 10(-12) in 1 s. The carbon nanotube laser frequency comb offers much promise as a robust and inexpensive all-fiber frequency comb with potential for scaling to higher repetition frequencies.