Is the Live Chats module available by default in the CRM?

No, it is not.
Before you start using Live Chats, you need to install the Vtiger Live Chat extension from the Extension Store. This step is mandatory as it enables the Live Chats module in the Essentials tab. Enabling the Live Chats module will allow your support team to use it as well as provide a platform for your customers to talk to your team. 
To learn more about Live Chats, click here.