this is considered custom programming.  You can use the console and look to see what css effects this and then put that css in your admin theme custom css section.  

Topic was moved from General Questions.

If you are wanting to shift the message box up from the bottom a little you can try this css. Setting the bottom margin will increase the space at the bottom.

.ow_chat_dialog_wrap .ow_mailchat_new_message.ow_chat_dialog {
    margin-bottom: 60px;
}