The adsorption of 1,4-cyclohexadiene on the Si(001) surface is studied by first-principles density-functional calculations within the generalized gradient approximation. The "pedestal" structure where the two C==C double bonds react with different Si dimers is found to be more stable than the "upright" structure where only one of the two C==C bonds reacts with a Si dimer. However, the [2+2] cycloaddition reaction can easily form the upright structure but not the pedestal one. The latter structure can be obtained from the former through a high energy barrier of similar to0.95 eV, indicating a small reaction rate at room temperature. Our results provide the theoretical basis for the interpretation of recent low-energy electron diffraction and photoelectron spectroscopy data in which the upright structure was seen.