The use of optical fiber in phased-array antennas beamforming networks offers several benefits, such as low losses, low weight, and wide instantaneous bandwidth. This paper proposes and describes a novel approach to true-time delay optical feeders for phased-array antennas. A compact, continuously variable, true-time delay unit is created by employing a reduced tuning-range tunable laser and one wide-bandwidth, chirped fiber grating as a dispersive element. The dispersion-induced distortion and bandwidth limitation is studied and different optical modulation schemes (AM, SSB+C, and self-heterodyne) are considered and measured.