What have you got sofar?
I would probably add an onClick handle to the checkbox. Something like:
<script>
function swappit(cb){
theDiv = document.getElementById('mydiv');
document.theDiv.style.visibility = (cb.checked)?'hidden':'visible';
}
</script>
<input type="checkbox" name="swapper" id="swapper" value="1" onclick="swappit(this)" />
<div id="mydiv" name="mydiv">blablabla</div>
