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");
});