Laser frequency combs are normally based on mode-locked oscillators emitting ultrashort pulses of ~100-fs or shorter. In this paper, we present a self-referenced frequency comb based on a narrowband (5-nm bandwidth corresponding to 415-fs transform-limited pulses) Yb-fiber oscillator with a repetition rate of 280 MHz. We employ a nonlinear Yb-fiber amplifier to both amplify the narrowband pulses and broaden their optical spectrum. To optimize the carrier envelope offset frequency (fCEO), we optimize the nonlinear pulse amplification by pre-chirping the pulses at the amplifier input. An optimum negative pre-chirp exists, which produces a signal-to-noise ratio of 35 dB (100 kHz resolution bandwidth) for the detected fCEO. We phase stabilize the fCEO using a feed-forward method, resulting in 0.64-rad (integrated from 1 Hz to 10 MHz) phase noise for the in-loop error signal. This work demonstrates the feasibility of implementing frequency combs from a narrowband oscillator, which is of particular importance for realizing large line-spacing frequency combs based on multi-GHz oscillators usually emitting long (>200 fs) pulses.