This for any chat, not just live chat.

The chat should be default minimized on page load and pops-open based on a rule. Options should be: open on page load, after X seconds on site, or after X percentage scrolled down the page. After X seconds on each page might be a good fourth wildcard option.

This REALLY increases conversion rates on chats. This was a clear incremental win in car sales and is probably applicable for all industries.