Do we have out of the box chatbot component available in 6.5?
I don't think we have one. But, you can refer to adobe published bot integration for web chatbots at . If its a JS based bot, you can simply manage via clientlibs or script calls.
 - https://github.com/adobe/aec-bot-integrations/tree/master/aem-chatbot-demo
You can look at using AWS Cloud Solutions in conjunction with AEM to build chat functionality. For example - https://aws.amazon.com/blogs/contact-center/reaching-more-customers-with-web-and-mobile-chat-on-amaz...
Livefyre apps provide chat feature and can be integrated to AEM: