In this note, we study the field generated by the traces of subgroups of ${\rm SU}(n,1)$. Under some hypotheses, the trace field of a group ${\rm \Gamma}\subset {\rm SU}(2,1)$ is equal to the field generated by the coefficients of the matrices in ${\rm \Gamma}$. If the group is the image of a representation of the fundamental group of a triangulated $3$-manifold, we can relate the trace field to a geometric invariant. For an arithmetic group of the first type in ${\rm SU}(n,1)$, up to conjugacy, the trace field and the field of the coefficients are the same.