The JSONObject loads a json file from a data folder or a URL.  In your case, your results are not a file.

Good advice from benj.n.sugar.
For the record, if you really need to load a Json string, you can:
JSONObject json = JSONObject.parse(someString);
In your case, telling to load the data directly from the file is faster and simpler.

Okay, I tried doing this instead:

Is there a difference between
processing stzable 2.0 and
Beta 2.09b?

Because I also get the error (JSONObject unknown) with just:

1. JSONObject xivelyData ;

in Beta 2.09b

I get no errors on JSONObject with 2.0 stable.
And you have to use a specialized get: getString(), getInt(), getFloat(), etc.
And the JSONObject functions no longer throw exceptions.
This works (more or less) for me:

1. void setup() {
2.   getData(); //Retrieve feed from Xively
3. }
4.  
5. void draw() {
6. }
7.  
8. void getData() {
9.   String request = baseUrl + feedId + ".json?key=" + apiKey + "&start=" + startDate + "&interval=3600&interval_type=discrete"; //request an hourly breakdown
10.   String result = join(loadStrings(request), "");
11.  
12.   // Create a new JSON object with our xivelyData feed
13.   JSONObject xivelyData = JSONObject.parse(result);
14.   println(xivelyData.getString("location"));
15.  
16.   JSONArray streams = xivelyData.getJSONArray("datastreams");
17.   println(streams);
18. }

Note: no need for semi-colons after a closing brace (in general).
I get an error from the server, but I suppose it is OK:
java.io.IOException: Server returned HTTP response code: 401 for URL: https://api.xively.com/v2/feeds/12404096571240409657.json?key=myKoV3FlYlXwViehe0bDrloiz2OaewxXiahTaSEDsKbXqxSv&start=2013-06-10T13:56:14.136746Z&interval=3600&interval_type=discrete

Thanks!