You can add a function in your javascript library to grab all text and put it in a textbox, which on a browser like chrome will then trigger the native spellchecker.
function SpellCheck()
{
var ta=document.createElement('textarea');
var s=document.createAttribute('style');
s.nodeValue='width:100%;height:100em;';
ta.setAttributeNode(s);
ta.appendChild(document.createTextNode(document.body.innerText));
document.body.appendChild(ta);
ta.focus();
for (var i = 1; i <= ta.value.length; i++)
ta.setSelectionRange(i, i);
}
Code from @JohnLBevan blog post (posted on 2011/03/28)