How to make the screen blink when there is an unread message

Instead of creating a Chrome plugin, I would either start the window title or use HTML5 notifications. Create a simple page that polls your Gmail IMAP for new messages and includes gmail in a large iFrame. If a new message is found, your external window may issue a notification.

HTML5 notifications : http://www.html5rocks.com/en/tutorials/notifications/quick/

Blinking header (adopted from this ):

var newMailBlinker = (function () {
    var oldTitle = document.title,
        msg = 'New Mail!',
        timeoutId,
        blink = function() { 
            document.title = document.title == msg ? ' ' : msg; 
        },
        clear = function() {
            clearInterval(timeoutId);
            document.title = oldTitle;
            window.onmousemove = null;
            timeoutId = null;
        };

    return function () {
        if (!timeoutId) {
            timeoutId = setInterval(blink, 1000);
            window.onmousemove = clear;
        }
    };
}());

PHP Gmail IMAP poll (adopted from this ):

$t1=time();//mark time in
$tt=$t1+(60*1);//total time = t1 + n seconds

do{
    if(isset($t2)) unset($t2);//clean it at every loop cicle
    $t2=time();//mark time
    if(imap_num_msg($imap)!=0){//if there is any message (in the inbox)

        $mc=imap_check($imap);//messages check
        //var_dump($mc); die;//vardump it to see all the data it is possible to get with imap_check() and them customize it for yourself
        echo 'New messages available';

    }else echo 'No new messagens';

    sleep(rand(7,13));//Give Google server a breack
    if(!@imap_ping($imap)){//if the connection is not up
        //start the imap connection the normal way like you did at first
    }

}while($tt>$t2);//if the total time was not achivied yet, get back to the beginning of the loop

jQuery AJAX Poll to your IMAP script (adopted from this ):

// make the AJAX request
function ajax_request() {
  $.ajax({
    url: '/path/to/gmail/imap/checkMessages.php',
    dataType: 'json',
    error: function(xhr_data) {
      // terminate the script
    },
    success: function(xhr_data) {
        console.log(xhr_data);
        if (xhr_data.status == 'No new messages') {
            setTimeout(function() { ajax_request(); }, 15000); // wait 15 seconds than call ajax request again
        } else {
            newMailBlinker(); // blink the title here for new messages
        }
    }
    contentType: 'application/json'
  });
}

, jQuery PHP . , . , , PHP IMAP . .