To Enable Notifications for Client Portal chat there are two components to it. The first is to enable notifications on your MSP Process account. You can do this by going to the profile icon in the top right next to your name as shown below: 

Turn on and set your email or SMS notification preferences: 

Then go to Client Portal -> Configurations and edit your configuration as shown below: 

Enable Notifications and set it to 1 min for the fastest notification. Then click one or more users who will get notified on inbound client portal chat requests. 

Click Submit. If you select more than 1 user the system will round robin notifications.