I second, to the wonderful suggestions shared by the members and seniors above which can provide you the solution of your problem, would like to share myself but before going further I have few questions for you, kindly answer the following.
-how many departments you have in your company?
-share the total employee strength,
-please share the percentage of employees you found are busy with "chitchat"
-is there any employee consultation/motivation program you (employer) have introduced to tackle the problem
-or share if there is any activity such as "Fun at work" or kind of program ever adopted by your employer
-please share something about you and your total/present experience with this company.
Sometime what we feel about our work and responsibilities towards our company/ organization, being an authority we expect the same from other/ employees too, but it doesn't mean that all can feel the same or we forced them to do so all the time. Therefore, it is really important to understand the situation/problem with patience and need to spent time by analyzing the causes of it.
Hope there is nothing like you are taking this activity too seriously because some of discussions/chat we all are doing at our work place which cant be stop permanently at any cost as we are the social entity and cant always discuss the same or particular things related to work. And I believe no one here can deny of this fact too.
Second, It is good that you want to improve the productivity of company and wish to create a good work atmosphere, you must do something that make them all feel comfortable with work and sense of responsibility which is enough to get good results. Because you also have accepted that the most of employees are performing good and achieving their assigned daily targets, but some of them are still busy in doing 'ChitChat'. To control this, you must make them busy with their work as much as possible which can be done by "Workload Analysis" or by assigning more work to them, so that, they have less time to discuss other things then related to work but must always take care of their comfort too.
Have you ever thought of introducing a 'Consultation and Motivation' program for your employees (a penal of TLs/Seniors/ HODs internally can be used for this or any reputed external agency if you can bear the expenses) that can help you in knowing them better just like about their work and performance by workload analysis. Also the "Employee of the Month" program can help you in this if it has still not been adopted by you.
You not just need to control 'Chit Chat" in office but to boost moral, sense of work responsibility, have to create a healthy work atmosphere by making them happy at work.
By "Fun at work" weekly activity can create creativity and positive emotions that helps in 'employee engagement' and good results.
Best of Luck