Burp Suite is a Java (desktop) app it looks like? I doubt you can replicate the full functionality on a Chrome extension, and particularly for modify & resend HTTP requests, this was taken off the Burp Suite site:
An intercepting Proxy, which lets you inspect and modify traffic between your browser and the target application.
so it uses a proxy. You likely can't embed a proxy as part of Chrome extension. And Chrome developer tools interface shows you network requests but I don't think you can alter requests nor resend them.
So the general answer is no. However, you could be able to "replay" HTTP requests captured in an archive file. e.g. Apache/web server logs, or a HAR file capture of network requests from browser (pulled from a proxy server like BrowserMob proxy or from browser itself like Chrome has option to extract network requests as HAR file).
You then simply need to build an extension that reads the HAR file or server log file that you supply then for each logged request, create an XmlHttpRequest (or jQuery AJAX request) that replicates that request (reconstructing the cookies, headers, content, as stored/logged in the file). This I'm assuming Chrome extensions allow you to read files on localhost filesystem if you provide a browse for file dialog.
And on a related note, while you can't modify web requests from within Chrome, extension or not, I believe you can modify cookies (so that subsequent requests will send the modified cookie). The cookie modification is either availble built-in to Chrome or via some Chrome extension. I'm not sure. But I know you can edit from Firefox using Firebug or FireCookie.