Is there a way to automatically email the chat transcript after chat is terminated?

Environment:

Chat - End-user Pages, Customer Portal, Incident Rule

Resolution:

In order for chat transcripts to be sent to customers, the chat session must first be saved as an incident. Then, you can configure an incident rule that sends a response to the end-user.

Step 1

You will need to append a response to the incident so that the email could be properly formatted.  So this can be done without agent interaction, create a standard text for rules by navigating to Service Configuration > Content Library > Standard Text.  Once the editor is open, create a new standard text. Make sure the ‘Rule Text’ check box is checked and add some text that states something to the effect of: “Thank you for taking the time to chat with us. We are appending a copy of your chat transcript for future reference”.

Step 2 

Create an incident rule that will act on the incidents that are created from your chat sessions based on the incident source field. A basic example of such a rule is:

IF
Incidents.Source equals Live Chat

THEN
1. Append Response Template to Response Field  (Select the standard text that you created above).
2. Send Email Response to Sender (enable the Include Question and Include Incident Details checkboxes)

Add other additional actions as necessary such as assigning the incident to a specific group, setting Product or Category values,  setting the status and setting a Transition State.

Once you have added the rule, be sure to compile and activate the rule set.

Step 3

Make sure the Incident Thread is added to the relevant message template.

Navigate to Site Configuration > Message Templates > Select the interface >  Contact Emails in the top ribbon >  Rules > Edit  > Click inside the body and on the left side you will see Incident Thread. Add it, afterwards double click on it and make sure Chat Transcript is checked  > Save it > Deploy the change > Save the Message Template.

See Answer ID 11857 for additional details: Message template used when rules trigger a response

Finally, you should create a test chat session to verify that the response is being sent out as expected.