Someone by the name of Alpha wrote up a great article on how to accomplish this here:

http://wupeng.cn/post/2009/08/27/Add-Captcha-to-BlogEngineNet.aspx

There is, however one fix I had to do in order to make it work.

In the CommentView.aspx page (Step 2.2) for BE 1.6 this code does not work.  Instead you need to use this tag for the Input control (btnSaveAjax):

<input type="button" id="btnSaveAjax" value="<%=Resources.labels.saveComment %>"
 onclick="if(Page_ClientValidate('AddComment')&&checkCaptchaResult){BlogEngine.addComment()}"
 tabindex="7" />

Thanks to Bryian Tan for posting this fix in the comments section of Alpha’s blog.