We have recently found that the negative thermal expansion (NTE) materials, ZrW2O8 and HfMo2O8, show exceptionally low thermal conductivity. We surmise that the mechanism is the efficient coupling of the low-frequency optic phonons that give rise to negative thermal expansion with the heat-carrying acoustic phonons. Although neither ZrW2O8 nor HfMo2O8 has suitable electronic properties for thermoelectric applications, perhaps the principle of reduced thermal conductivity by low-frequency optic phonons in NTE materials can be used to develop more efficient thermoelectric materials.