Observations of magnetic reconnection between colliding plumes of magnetized laser-produced plasma are presented. Two counterpropagating plasma flows are created by irradiating oppositely placed plastic (CH) targets with 1.8-kJ, 2-ns laser beams on the Omega EP Laser System. The interaction region between the plumes is prefilled with a low-density background plasma and magnetized by an externally applied magnetic field, imposed perpendicular to the plasma flow, and initialized with an X-type null point geometry with B=0 at the midplane and B=8 T at the targets. The counterflowing plumes sweep up and compress the background plasma and the magnetic field into a pair of magnetized ribbons, which collide, stagnate, and reconnect at the midplane, allowing the first detailed observations of a stretched current sheet in laser-driven reconnection experiments. The dynamics of current sheet formation are in good agreement with first-principles particle-in-cell simulations that model the experiments.