gistfile1.html

<script type="text/javascript" charset="utf-8">
//in the HTML page, first include Prototype, then do this
document.observe('dom:loaded',function(){
  new Ajax.Updater(document.forms[0],'your-form-go.php',{parameters:{getKey:true},insertion:'top'});
});
</script>

<?php
//back in form-handler-land
function isAjax(){
  return (isset($_SERVER['HTTP_X_REQUESTED_WITH']) && 
    ($_SERVER['HTTP_X_REQUESTED_WITH'] == 'XMLHttpRequest'));
}
$keys = array('keyOne','keyFortyTwo');
$salt = 'some ferociously complex salt';
if(isAjax() && isset($_POST['getKey'])){
  $key = $keys[rand(count($keys) - 1)];
  header('Content-type: text/html; charset="utf-8"');
  print '<input type="hidden" name="' . $key . '" value="' . md5($key . $salt) . '"/>';
  exit;
}
$not_a_bot = false;
foreach($keys as $key){
  if(isset($_POST[$key]) && $_POST[$key] = md5($key . $salt)){
    //yay!
    $not_a_bot = true;
  }
}
if($not_a_bot){
  //proceed accordingly
}
?>