Hope these recommendations help. You can do an extensive search in the App store for more possible options but the ones in bold are the ones we currently utilizing for our Shopify store.
QuestionTime (beta) | https://apps.shopify.com/questiontime | $0.00/mo.
AnswerEasy Help Desk | https://apps.shopify.com/answerseasy | $0.00 - $5.00/mo.
Helpjuice | https://apps.shopify.com/helpjuice | $0.00 - $99.00/mo.
viCloning | https://apps.shopify.com/vicloning | $0.00 - $299.00/mo. (we are paying $199.00/mo.)
You may also hire your own customer service department for $5/hr. This company will answer emails, live chat requests and phone calls every day of the week to help you concentrate on growing your Shopify business | https://apps.shopify.com/5-hour-customer-support