Get a Hangout App for your Chrome to keep you update with the messages which been send and receives for you . 
How to Get app , follow the following steps .
Step 1 : Visit the following link : 
Step 2 : In left hand-side menu more icon which is represent by three dots  … 
Step 3 : In the sub menu, click over Chromes from App downloads section

Step 4: A pop up window will show up as picture below , Click over Add app 
Step 5: When you go to Google Chrome Apps by type chrome://apps/ in address bar , you will find hangouts app waiting you to lunch it .