Circumventing the data rate bottleneck due to the bandwidth limitation of optical devices is an imperative for today's fiber-optic communication systems. This paper investigates a two-stage laser driver consisting of a precoder and an encoder stage, capable of applying duobinary modulation to a bandwidth-limited vertical-cavity surface-emitting laser (VCSEL). Thus, the transmitter's data rate capacity per cycle of bandwidth is significantly increased. By employing a cross-coupled architecture for the precoder stage, the output data rate of the driver is doubled with respect to the input data rate. Electro-optical measurements of the driver bonded to a VCSEL with inherent bandwidth of 20 GHz yielded duobinary eye diagrams at data rates up to 56 Gb/s, which represents a significant speed enhancement with regard to the laser's own bandwidth. To the best of the authors' knowledge, this is the fastest integrated duobinary VCSEL driver reported so far, as well as the first chip-to-chip integration of such an electrical driver with a VCSEL device.