Shopify Inbox

This is a great, free chat app. The "Quick Replies" function allows many pre-written answers to be looked up very quickly. Also, the built in product links show the customers photos of the product and allows quick lookups of your products.

The mobile app is fantastic as well.

The only thing I would change or add would be a feature to send a message to a customer who has not yet chatted - like a chat bubble that says "Ask us a question" so they can see the chat box more easily on the website.