Be sure to call .chosen()after dynamically populating the drop-down list.
Here is the fiddle https://jsfiddle.net/npzs2bt7/
EDIT 1:
You probably didn't call chosen()in the drop-down list before you could call trigger("chosen:updated").
https://jsfiddle.net/npzs2bt7/1/
2:
Jquery 1.9.0, Chosen.Jquery 1.1.0
html (chosentest.html) .
<html>
<head>
<title>chosen demo</title>
<link rel="stylesheet" type="text/css" href="https://cdnjs.cloudflare.com/ajax/libs/chosen/1.1.0/chosen.min.css">
<style type="text/css">
#test
{
width:100px;
}
</style>
</head>
<body>
<select id="test" class="chosen-select">
<option>Select1</option>
</select>
<button class="btn">Click to see selected value</button>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.9.0/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/chosen/1.1.0/chosen.jquery.min.js"></script>
<script type="text/javascript">
$(document).ready(function() {
$("#test").chosen();
var div2=[];
div2.push("<option value='1'>ALL1</option>");
div2.push("<option value='2'>ALL2</option>");
div2.push("<option value='3'>ALL3</option>");
div2.push("<option value='4'>ALL4</option>");
div2.push("<option value='5'>ALL5</option>");
$("#test").html(div2.join(''));
$("#test").trigger("chosen:updated");
$(".btn").click(function(){
alert($("#test").val());
});
});
</script>
</body>
</html>