I believe I came across one by Paul Johnston at http://pajhome.org.uk/crypt/md5/contrib/sha1_stream.js . It is listed on the page http://pajhome.org.uk/crypt/md5/scripts.html . I have not tested it myself, but I have used his non-streamable version that he modified for it.
UPDATE: Here is some example code (I verified it against a separate SHA1 known to be correct). Make sure you include the original sha1.js (found at http://pajhome.org.uk/crypt/md5/sha1.js) before the streamable sha1_stream.js.
<script src="sha1.js" type="text/javascript" charset="utf-8"></script>
<script src="sha1_stream.js" type="text/javascript" charset="utf-8"></script>
<script type="text/javascript" charset="utf-8">
var input = 'abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz';
var blocksize = 512;
var h = naked_sha1_head();
for (var i = 0; i < input.length; i += blocksize) {
var len = Math.min(blocksize, input.length - i);
var block = input.substr(i, len);
naked_sha1(str2binb(block), len*chrsz, h);
}
var result = binb2hex(naked_sha1_tail(h));
</script>