This paper analyzes the relation of viability kernels and controlsets of control affine systems. A viability kernel describesthe largest closed viability domain contained in some closed subsetQ of the state space. On theother hand, control sets are maximal regions of the state spacewhere approximate controllability holds. It turns out thatthe viability kernel of Q can be represented by the union ofdomains of attraction of chain control sets, defined relativeto the given set Q.In particular, with thisresult control sets and their domains of attractioncan be computed using techniques for thecomputation of attractors and viability kernels.