An important example of hybrid organic-silicon systems is the fabrication of styrene molecular wires on a H-passivated Si(001) surface. Here we theoretically demonstrate that a styrene molecule which easily adsorbs on a single H-empty site can be further stabilized (with an energy barrier of 0.88 eV) by abstracting an H atom from a neighboring Si dimer. This H-abstraction process creates another H-empty site, setting off a chain reaction that results in the growth of a styrene wire along the Si dimer row. Our simulated scanning tunneling microscope (STM) image for the resulting one-dimensional (1D) molecular wire is in good agreement with STM data. In particular, the antibonding π orbitals on adjacent styrene molecules overlap, thus providing ``channels'' that permit charge transport along this 1D wire under a voltage bias.