Clear and refresh jQuery Chosen dropdown list

Using .trigger("chosen:updated"); you can update the options list after appending.

Updating Chosen Dynamically: If you need to update the options in your select field and want Chosen to pick up the changes, you’ll
need to trigger the “chosen:updated” event on the field. Chosen will
re-build itself based on the updated content.

Your code:

$("#refreshgallery").click(function(){
        $('#picturegallery').empty(); //remove all child nodes
        var newOption = $('<option value="1">test</option>');
        $('#picturegallery').append(newOption);
        $('#picturegallery').trigger("chosen:updated");
    });