Your example is perfectly correct and natural. Using ～の twice in a row is usual. (I am not so sure about particles other than の, but in this answer, I will focus on repetition of の.)
How about more repetitions? I agree with Dave M G that, as far as correctness is concerned, you can use as many ～の as you like. However, if a sentence uses ～の many times in a row, it starts to look strange. In general, using the same construct again and again is usually considered as a poor practice.
For example, if a hypothetical report is titled 敬語の用法の習得の困難さの原因の考察, it is understandable (“Consideration of Reasons for the Difficulty of Learning the Usage of Honorifics”) and probably most people agree that it is correct. (This example is partly based on rdb’s comment on Dave’s answer.) This example does not have an issue with ambiguity which Axioplase (rightly) raised. Nevertheless, this title is awkward because of the repeated uses of の. 敬語の用法の習得が困難である原因の考察 sounds better.
Some people even say that you should not use ～の three times in a row for good writing. Here is an example. However, funny part of that text is in its correction: one of the “good examples” in an older version of the text contained ～の three times in a row! I think that the lesson is that there is no firm rule about the number of times you can use ～の in a row in good writing, although unfortunately it does not seem that the author learned this lesson.