A charge-density-wave (CDW) ground state that exists in Nb3Te4 below 115 K is not observed in the isostructural and isoelectronic Nb3Se4 and Nb3S4. Intercalating indium into Nb3Se4 induces a Peierls transition to a CDW ground state near 35 K judging by a peak in the resistivity. The onset temperature of this resistance peak is influenced by the mole fraction intercalated. Electron diffraction (ED) evidence supports these findings. In contrast, intercalating Nb3S4 with indium does not produce a resistivity peak above similar to 12 K to suggest the presence of a CDW ground state. An electron diffraction study has linked complex superlattice satellites (SLS) near 90 K in both chalcogenides to a CDW transition but the present resistivity results suggest that this is not the case. A number of other guests intercalated into either chalcogenide do not produce any resistivity features to suggest a Peierls transition. A CDW does, however, appear to exist in Ga1.0Nb3Te4 and provides support for an apparent synergism between group III metals intercalated into Nb3Te4 and Nb3Se4 and the existence of a CDW ground state. Pulsed resistivity measurements of In1.0Nb3Se4 at 12 K with fields to similar to 20 V/cm indicate that the electrical transport remains ohmic.