Chemical vapor deposition (CVD) of indium nitride (InN) is severely limited by the low thermal stability of the material, and thus low temperature deposition processes, such as atomic layer deposition (ALD), are needed to deposit InN films. The two chemically and structurally closely related materials aluminum nitride (AlN) and gallium nitride (GaN) has been deposited by both plasma and thermal ALD, with ammonia (NH3) as nitrogen precursor in thermal processes. InN, however, has only been deposited using plasma ALD, indicating that there might be a limitation to thermal ALD with NH3 for InN. We use quantum-chemical density functional theory (DFT) calculations to compare the adsorption process of NH3 on GaN and InN to investigate if differences in the process could account for the lack of thermal ALD of InN. Our findings show a similar adsorption mechanism on both materials, in which NH3 could adsorb onto a vacant site left by a desorbing methyl group from the surfaces. The difference in energy barrier for this adsorption indicates that the process is many magnitudes slower on InN compared to GaN. The slow adsorption kinetics would hinder NH3 from adsorption onto InN in the timeframe of the ALD growth process and thus limit the availability of a thermal ALD process.