Classical optimization algorithms are insufficient in large-scale combinatorial problems and in nonlinear problems. Hence, heuristic optimization algorithms have been proposed. General purposed metaheuristic methods are evaluated in nine different groups: biology-based, physics-based, social-based, music-based, chemical-based, sports-based, mathematics-based, and hybrid methods which are combinations of these. Recently, a sports-based search and optimization algorithm entitled as league championship algorithm (LCA) has been proposed. LCA is a population-based, metaheuristic optimization algorithm that simulates a championship for general optimization with artificial teams and artificial league for several weeks. In this algorithm, according to the league program, a number is given to the couple of teams that will match and the result of match is determined as loser or winner. Winning or losing the game is closely related to power of teams. Teams are intended to improve the formation of the current team throughout the season to win the game in the coming weeks. Chaotic maps seem to improve the convergence speed and accuracy of optimization algorithms. Increasing global convergence speed and prevention of getting stuck on local solutions of LCA with chaos have been proposed for the first time in this study. In this paper, six different chaotic LCAs have been proposed and explained in detail. Comparative performance results have been examined in complex benchmark functions. Promising results have been obtained from the experimental results. Combining results appeared in different fields like LCA and complex dynamics can increase quality in some optimization problems and the chaos can be the wanted process.