jQuery Check if Checkbox is Checked, then Add Value to Input Field

I have a shopping cart checkout page and I'm trying to add a "gift" option. What needs to happen: Once the checkbox is selected for "Send Order As Gift", a value needs to be assigned to a hidden input field so that the information is moved onto the confirmation page and various receipts.

HTML:

<h3>Send Order As Gift</h3>
<ul>
    <li class="fc_row fc_gift"><label for="gift" class="fc_pre">This is a gift, 
    please do not include a receipt.</label>
    <input type="checkbox" name="gift" id="gift" class="checkbox" value="" />
    <input type="hidden" name="Gift" id="gift-true" value="" /></li>
    <script type="text/javascript">
    $(document).ready(function(){
        $("#gift-true").input( $('#edit-checkbox-id').is(':checked').val() + "Yes"); 
    });​                
    </script>
    </li>
    <li class="fc_row fc_gift_message"><label for="Gift Message">Include a message 
    (limit 100 characters):</label>
    <textarea name="Gift Message" cols="50" rows="3" maxlength="100"></textarea>
    </li>
</ul>