This is one of the most common issues for newbie users and the solution is quite simple.
Most of the people deploy the chat button on the position "right button" and the proactive invitation by default use the same position on the site, the solution is to change the position for the proactive invitation.
How to fix :
1. Go to the Live Chat Server dashboard
2. Go to the section "server settings"
3. Update the setting "proactive message position"
4. Save the settings and try again.
Remember if you are testing the site often is better to clear up the browser cookies and cache for your site after any change on the Live Chat configuration.