Using a first-principles pseudopotential method we have studied the adsorption and dissociation of NH3, PH3, and AsH3 on the Si(001)-(2x1) surface. Apart from the existence of a barrier for the adsorption of the precursor state for arsine, we observe that the global behavior for the chemisorption of the XH3 molecules considered in this work is as follows: the gas phase XH3 adsorbs molecularly to the electrophilic surface Si atom and then dissociates into XH2 and H, bonded to the electrophilic and nucleophilic surface silicon dimer atoms, respectively. The energy barrier, corresponding to a thermal activation, is much smaller than the usual growth temperature, indicating that all three molecules will be observed in their dissociated states at room temperature. All adsorbed systems are characterized by elongated Si-Si dimers that are (almost) symmetric in the dissociative case but asymmetric in the molecular case. According to our first-principles calculations, all XH3 and XH2 systems retain the pyramidal geometry observed for the gas molecules. Our calculated vibrational spectra further support the dissociative model for the XH3 molecules considered here.