The chemisorption of C8H8 bicyclo[2.2.2]-2,5,7-octatriene (barrelene) on the Si(100) surface is studied from first principles calculations. We find that, in the most stable configuration, barrelene is bonded to Si(100) through four Si-C bonds, with the C-C bonds which are orthogonal to the underlying Si dimers. The chemisorption reaction responsible for this structure is driven by the biradical nature of the Si-Si dimer bond. Two others, slightly less stable configurations, exist which are also characterized by four Si-C bonds but have a different orientation or location with respect to the Si(100) surface. The properties of these and other, less stable configurations have been investigated. For the most stable structures, the effect of different surface coverages has been also studied, showing a tendency to easily form complete monolayers of barrelene on the Si surface. On the basis of energetic and kinetic considerations, we expect that chemisorption of barrelene monolayers on the Si(100) surface will be characterized however by a certain amount of disorder. Finally, several possible reaction pathways, leading from one stable structure to another of lower energy or from a molecule in the gas phase to a chemisorbed configuration, have been investigated in detail and estimates of the relative energy barriers are given.