We compute the motivic Donaldson-Thomas invariants of the one-loop quiver, with an arbitrary potential. This is the first computation of motivic Donaldson-Thomas invariants to use in an essential way the full machinery of (mu) over cap -equivariant motives, for which we prove a dimensional reduction result similar to that of Behrend, Bryan and Szendroi in their study of degree- zero motivic Donaldson-Thomas invariants. Our result differs from theirs in that it involves nontrivial monodromy.