Yep. You will need a plugin to add the chat box functionality to your WordPress.com site: firesticksbestbuilds2018.wordpress.com
In order to use plugins we have to change the site infrastructure and our business plan is required for that. In addition to your custom domain and hosting, it also includes 24/7 support via live chat. Check it out at https://wordpress.com/plans/
If upgrading is not the right choice then you could always use a contact form for free. That can be added to any page, post, or even widget area on the site. When that form gets submitted you’ll receive it via email and can reply to the user directly.