According to the website of the chemistry department at the University of Wisconsin, a chlorine atom can make a single covalent bond. Chlorine atoms have seven electrons in their outer shells and can only share one electron with another element.
By which columns the elements are arranged, the periodic table displays the number of bonds required to fill electron shells. The column for elements with seven electrons in their outer shells contains chlorine. Additionally, chlorine is a strongly electronegative element, meaning it hangs onto its electrons securely. Therefore, even if it shares its single electron with another atom in a covalent link, the other electrons are unavailable for the formation of new bonds.