Fitness Dependent Optimizer (FDO) is a recent metaheuristic algorithm that mimics the reproduction behavior of the bee swarm in finding better hives. This algorithm is similar to Particle Swarm Optimization (PSO) but it works differently. The algorithm is very powerful and has better results compared to other common metaheuristic algorithms. This paper aims at improving the performance of FDO, thus, the chaotic theory is used inside FDO to propose Chaotic FDO (CFDO). Ten chaotic maps are used in the CFDO to consider which of them are performing well to avoid local optima and finding global optima. New technic is used to conduct population in specific limitation since FDO technic has a problem to amend population. The proposed CFDO is evaluated by using 10 benchmark functions from CEC2019. Finally, the results show that the ability of CFDO is improved. Singer map has a great impact on improving CFDO while the Tent map is the worst. Results show that CFDO is superior to GA, FDO, and CSO. Both CEC2013 and CEC2005 are used to evaluate CFDO. Finally, the proposed CFDO is applied to classical engineering problems, such as pressure vessel design and the result shows that CFDO can handle the problem better than WOA, GWO, FDO, and CGWO. Besides, CFDO is applied to solve the task assignment problem and then compared to the original FDO. The results prove that CFDO has better capability to solve the problem.