  Given a link $L\subset S^3$, a representation $\pi_1(S^3-L)\to{\rm
SL}(2,\mathbb{C})$ is {\it trace-free} if it sends each meridian to an element
with trace zero. We present a method for completely determining trace-free
${\rm SL}(2,\mathbb{C})$-representations for arborescent links. Concrete
computations are done for a class of 3-bridge arborescent links.
