Yes, this is possible with the help of a Gmail lab feature called Right-side Chat. The Right-side Chat lab feature will allow you to move the Chat box in your Gmail from left-side to the right-side. The lab feature once enabled, will place your chat box to the right side of the mail conversations.
1) In your Gmail account, click on the Mail Settings option.
2) In the Mail Settings window thus opened, click on the Labs tab.
3) Now, scroll down a little bit to find the Right-side Chat lab feature and once you find it, click on theEnable option that is displayed next to it.
4) Now, navigate to the bottom of the page that you are in and click on the Save changes button.
5) Once you click on the save changes button, you will be directed to your Gmail Mailbox and you can see that the Chat box is now placed on the right-side of your Gmail page, next to the mail conversations.
NOTE: - The Right-side Chat lab feature will not work if you have the Preview Pane lab feature enabled for your Gmail account. Preview pane lab feature will allow you to see a preview of your mail conversations when you click on a certain mail in your inbox. So, make sure that the Preview pane feature is not enabled in the labs settings page before you can make use of the Right-side lab feature to have your Chat box displayed on the right-side.
