The design of a solar PV system and its performance evaluation is an important aspect before going for a mass-scale installation and integration with the grid. The parameter evaluation of a solar PV model helps in accurate modeling and consequently efficient designing of the system. The parameters appear in the mathematical equations of the solar PV cell. A Chaos Induced Coyote Algorithm (CICA) to obtain the parameters in a single, double, and three diode model of a mono-crystalline, polycrystalline, and a thin-film solar PV cell has been proposed in this work. The Chaos Induced Coyote Algorithm for extracting the parameters incorporates the advantages of the conventional Coyote Algorithm by employing only two control parameters, making it easier to include the unique strategy that balances the exploration and exploitation in the search space. A comparison of the Chaos Induced Coyote Algorithm with some recently proposed solar photovoltaic cell parameter extraction algorithms has been presented. Analysis shows superior curve fitting and lesser Root Mean Square Error with the Chaos Induced Coyote Algorithm compared to other algorithms in a practical solar photovoltaic cell.