We demonstrate an all-optical tunable pulse delay scheme that utilizes the power-dependent variation of the refractive index that accompanies stimulated Raman scattering in an optical fiber. Using this technique, we delay 430-fs pulses by up to 85% of a pulse width. The ability to accommodate the bandwidth of pulses shorter than 1 ps in a fiber-based system makes this technique potentially viable for producing controllable delays in ultra-high bandwidth telecommunication systems.