To determine if a species is paramagnetic, we must check for the presence of unpaired electrons in its electronic configuration . Paramagnetism arises from the presence of unpaired electrons, while diamagnetic substances (which are not paramagnetic) have all electrons paired.

1. Cu^{2+} (Copper ion): The atomic number of Cu is 29. Its electronic configuration is [Ar] 3d^{10} 4s^{1}. For Cu^{2+}, two electrons are removed (one from 4s, one from 3d), resulting in [Ar] 3d^{9}. This configuration has one unpaired electron . Thus, Cu^{2+} is paramagnetic.
2. Fe^{2+} (Ferrous ion): The atomic number of Fe is 26. Its electronic configuration is [Ar] 3d^{6} 4s^{2}. For Fe^{2+}, two electrons are removed from the 4s orbital, resulting in [Ar] 3d^{6}. According to Hund's rule, this configuration has 4 unpaired electrons . Thus, Fe^{2+} is paramagnetic.
3. Cl^{-} (Chloride ion): The atomic number of Cl is 17 ([Ne] 3s^{2} 3p^{5}). The chloride ion (Cl^{-}) is formed by gaining one electron, resulting in the stable noble gas configuration of Argon: [Ne] 3s^{2} 3p^{6} or [Ar] . All electrons in this configuration are paired. Therefore, Cl^{-} is diamagnetic, meaning it is not paramagnetic.

Conclusion: Cl^{-} is the species that is not paramagnetic.