Hydroamidation of olefins constitutes an ideal, atom-efficient method to prepare carboxylic amides from easily available olefins, CO, and amines. So far, aliphatic amines are not suitable for these transformations. Here, we present a ligand- and additive-free Rh(I) catalyst as solution to this problem. Various amides are obtained in good yields and excellent regioselectivities. Notably, chemoselective amidation of aliphatic amines takes place in the presence of aromatic amines and alcohols. Mechanistic studies reveal the presence of Rh-acyl species as crucial intermediates for the selectivity and rate-limiting step in the proposed Rh(I)-catalytic cycle.