Contact both the customer and BBB to clarify the complaint and confirm it was intended for you. You can delight both parties by accepting responsibility and expressing empathy, even if you are not at fault. There is a long-told customer service story about Nordstrom accepting an faulty car tire...
Most live chat tools are encapsulated in a Javascript snippet to add to your site. WordPress, for example, may provide a plugin + if you look at the plugin code, usually the code simply injects the Javascript snippet. This said, all you really require... choose how you'd like the live chat icon...