This Letter describes the first experimental demonstration of the guiding of a relativistic electron beam in a solid target using two colinear, relativistically intense, picosecond laser pulses. The first pulse creates a magnetic field that guides the higher-current, fast-electron beam generated by the second pulse. The effects of intensity ratio, delay, total energy, and intrinsic prepulse are examined. Thermal and Kα imaging show reduced emission size, increased peak emission, and increased total emission at delays of 4-6 ps, an intensity ratio of 10∶1 (second:first) and a total energy of 186 J. In comparison to a single, high-contrast shot, the inferred fast-electron divergence is reduced by 2.7 times, while the fast-electron current density is increased by a factor of 1.8. The enhancements are reproduced with modeling and are shown to be due to the self-generation of magnetic fields. Such a scheme could be of considerable benefit to fast-ignition inertial fusion.