In this paper, a chaos driven Discrete Artificial Bee Algorithm is introduced. The main premise of this work is to ascertain if using chaos maps in lieu of standard pseudorandom number generators can improve the performance of the canonical algorithm. Nine unique chaos maps are embedded in the Discrete Artificial Bee Algorithm alongside the Mersenne twister and evaluated on the lot-streaming flowshop scheduling problem with setup time. Based on the obtained results, a number of chaotic maps significantly improve the performance of the algorithm. Additionally, the new algorithm is favourably compared with the chaos driven Enhanced Differential Evolution algorithm for the same problem.