We discuss this with him, and he understands the teachers need him to be quiet. His behavior may improve for a few days, but then he slips again. His grades are good. Almost all As a few Bs. He's bright and outgoing with a good personality.
Many teachers tape a piece of paper divided into time periods on the child's desk. The time periods would depend on the child's age: it could be divided by subjects, by hours, or whatever works. When the teacher goes by the desk she or he will put a check mark in the time period if the child is not talking. A silent cue could be used when he is talking (a touch on the shoulder, the teacher clearing his or her throat) to remind him to stop.
The key to helping with this issue is consistently dealing with the problem and providing immediate consequences and rewards. Decide with the teacher in advance how many checks are needed to make it a good day, and ask the teacher to send home each day a note or message in your son's planner. This could be as simple as a smiley face or a "Good day." Then follow up at home.
Three out of five good days in a week could mean extra computer or TV time or having a friend over to spend the night. Less than three out of five good days could mean not going to a special event over the weekend. The expectations could be raised as the talking improves.
If the problems persist, enlist the help of your son's school counselor, who could help by working with the teacher to set up a more specific behavior plan.