Create an effective seating arrangement. This may mean not only shifting students from one seat to another, but changing the layout of the tables or desks in your room. Try spacing out clusters of seats from each other. Assign each cluster at least one student whom you have found to be responsible and will encourage his classmates not to talk. Space students who are most prone to chatting as far from each other as you can, but do not isolate them from the rest of the class.
Create a discipline program, or if one is already in place, enforce it strictly. One example would be the "stop light" system, where students have color-coded cards to keep track of their behavior, with green being good, yellow being problematic and red being poor behavior. If students begin chatting during class, give them one warning, then have them change their card on the next incident. Repercussions for these cards, such as lost time during recess or calls to parents, need to be enforced, or the system will not have any influence on student behavior.
Provide positive feedback for good behavior. Positive feedback about proper social behavior should always be specific. For example, you could say, "I like the way Joey is doing his coloring quietly." This could be followed up with a gold star on a chart for good behavior, which can be tied to a reward system if you choose. Feedback also needs to be given consistently, not just to contrast one student's good behavior with other students' poor behavior. Set a goal for yourself of praising the behavior of at least four students every half day.
Talk to parents if a student has a particularly persistent problem with chatting in class. Most parents will be more than willing to talk to you if you let them know you are trying to help their child learn better, not single them out for punishment or embarrassment. You can work out a plan with the parents to help the particular student improve his behavior by setting short-term, reasonable goals. One possible goal is to go one day with only one or two reminders to stop talking. Send daily feedback to parents so they can encourage the student to improve as well.