It's not quite rikaichan, but there's Wakaru.
It has a built in browser with functionality similar to rikaichan, but I haven't really used it that much so can't really comment on it. I find the browser a bit fiddly to use, to be honest.
However, one of its other features is a built in ebook reader with the ability to directly download free books from a couple of online libraries. Once you have them then you can read them "rikaichan style" by highlighting words or phrases and getting popup definitions.
As an alternative to the above, you can copy/paste text to its clipboard and get popup help with that as well. Actually, this is the main way I use it, by copy/pasting entire stories from the likes of
http://hukumusume.com and "creating" my own books to read.
It's not free, but it's one of the best Japanese learning apps I've come across.