We report what we believe to be the first radiation-balanced fiber amplifier-a device that provides optical gain while experiencing no temperature rise. The gain medium is a silica fiber with a 21-μm-diameter core highly doped with Yb^{3+} (2.52 wt. %) and codoped with 2.00 wt. % Al to reduce concentration quenching. The amplifier is core pumped with 1040-nm light to create anti-Stokes fluorescence cooling and gain in the core at 1064 nm. Using a custom slow-light fiber Bragg grating sensor with mK resolution, temperature measurements are performed at multiple locations along the amplifier fiber. A 4.35-m fiber pumped with 2.62 W produced 17 dB of gain, while the average fiber temperature remained slightly below room temperature. This advancement is a fundamental step toward the creation of ultrastable lasers necessary to many applications, especially low-noise sensing and high-precision metrology.