Looking at your fiddle page, there might be some issues with the mouse events being detected due to the complication of the code aside from this part, however using this should get you most of the way there:
$(function() {
$(".chzn-select").chosen();
$('a').click(function() {
$('.mydiv').removeClass().addClass('redbrd mydiv');// NOTE this is in case your other question comes into play with this one.
});
$('body').on('mouseenter', '.redbrd', function() {
$('body').append('<div class="mmt">some text</div>');
});
$('body').on('mouseleave', '.redbrd', function() {
$('.mmt').remove();
});
});
EDIT: After review, your adding li to the page after your chosen thing.
This should work with that:
$(".chzn-select").chosen();
$(function() {
$('a').click(function() {
$('.mydiv').addClass('redbrd');
$('.redbrd').on('mouseover', 'li', function(e) {
var $target = $(e.target);
if ($('#mmt').length === 0) {
var htm = '<div id="mmt">' + $target.text() + ' some text</div>';
$('body').append(htm);
}
});
$('.redbrd').on('mouseout', function() {
$('#mmt').remove();
});
});
});
Updated your fiddle here:http://jsfiddle.net/JtQHY/1/ so you can test it.