you could put the text area into a span, and have the JS function change the style of the span by ID.
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>Untitled Document</title>
<script>
function toggleTextArea() {
var theForm = document.form1;
var theCheck = theForm.checkbox;
var theTextArea = document.getElementById('textAreaSpan');
if(theCheck.checked == true) {
theTextArea.style.display = "block";
} else {
theTextArea.style.display = "none";
}
}
</script>
</head>
<body>
<form id="form1" name="form1" method="post" action="">
<label for="textfield"></label>
<input type="text" name="textfield" id="textfield" />
<input name="checkbox" type="checkbox" id="checkbox" onchange="toggleTextArea();" value="1"/>
<label for="checkbox"></label>
<span style="display: none;" id="textAreaSpan"><label for="textfield2">label for text area</label>
<textarea name="textfield2" rows="8" id="textfield2"></textarea></span>
</form>
</body>
</html>