The balanced chemical equation is this:
Cl2(aq) + 2Br-(aq) --> 2Cl- + Br2(aq)
Looking at each substance involved in the reaction:
Cl2 has 0 charge and gains a charge of -1 after the reaction
Br- has a charge of -1 but turns to 0 after the reaction
Cl2 gained an electron which means it is the reduced substance
Br- lost an electron which means it is the oxidized substanced
Consequently, Cl2 is the oxidizing agent and Br- is the reducing agent.
