Add this to the bottom of your "Chat Connected Screen" theme to automatically redirect users to your email form if they've waited over 3 minutes for an agent to accept their chat.

gistfile1.html

<script>
var timeout = 180000;
var redirectTo = "/customer/portal/emails/new";
setTimeout('redirectToEmail()', timeout)
function redirectToEmail()
{
  if( "none" == $("#chat_send_area").css('display')) {
    alert("We're sorry, but we are no longer available to chat at this time. To leave us a note, just fill out the contact form on the next screen.");
    window.top.location.href = redirectTo; 
  }
}
</script>