The ALICE experiment is designed to study the properties of hadron and nucleus collisions in a new energy regime at the Large Hadron Collider at CERN. A fundamental observable in such collisions is the multiplicity distribution of charged particles. A forward multiplicity detector has been designed to extend the charged particle multiplicity coverage of the ALICE experiment to rapidities of -3.4<y<-1.7 and 1.7<y<5.0. This detector consists of five rings, each containing 10240 Si strips, divided into sectors comprised of Si sensors bonded and glued to hybrid PC boards equipped with radiation hard preamplifiers. The output of these preamplifiers is multiplexed into custom-made fast ADC chips located directly behind the Si sensors on the detector frame. These ADCs are read out, via optical fibers, to a data acquisition farm of commodity PCs. The design and characteristics of the ALICE Forward Multiplicity Detector will be discussed.