Chess 960 isn't supported right now. We have the automatic 960 set up for set piece games, but no support for 960 castling rules.
We are going to spend some time looking at the impact of introducing it properly though. It will be done, but it is not a quickie as this site was not built for variant support.
I somewhat prefer the castling rules for chess 480 (given in chess 960 under wikipedia).
However, whatever the castling rule used (960 or 480) it is exactly equivalent to the standard rule if the pieces start on the usual squares. Therefore I would have thought all that needed to be done from a coding point of view would be to generalise the RHP castling logic so that it worked for both normal chess and the chosen variant, there would be no need to have two rules implemented in RHP and switch between them.
In notation I suppose "king castles to left@ and "king castles to right" would be marked in notation as king side and queen side castling respectively, even if the queen happened to be somewhere not between the two rooks. This would keep the notation logic the same between standard and normal chess too.
One other potential difference is that at the start of the game record the starting position of the pieces must be recorded as a fen or whatever in order for the game to be replayable. However this could be done for normal chess too (again to keep the logic the same).
Of course this ignores the work to keep track separately of what game was played in league tables etc. They haven't managed this on instantchess.com where I play chess 960 and normal chess sometimes. Both games affect the same rating.
It may be complicated but I personally really like randomised chess because it makes the opening play much more interesting. It would be great if there were chess 960 tournaments! (hmm, would all games in a tournament group need to be given the same starting position, do you think?)