Yeah, either that or the fifty moves rule (in those situations where the king is chased over the whole board).
But you have to make the moves first to claim, you can't stop the clock and show the arbiter that it's impossible for him to get out of the checks.
Actually, either player may stop the clocks in order to summon the arbiter but if the arbiter decides you didnt have a legit cause to do so you can get a penalty against you. Also, whoever stops the clocks , it must be their move. You cannot stop the clocks if its your opponents move.
The first part makes sense, but why the second? You're only ever actually stopping one of the clocks, and when it's your opponent's move it's his clock you're stopping. If it was my move I certainly wouldn't take issue with my opponent stopping my clock.
Is it possibly just out of consideration for your opponent's concentration?
Uhm... I thought a few years ago (round about the time rule 10.2 was introduced). I distinctly recall it being a rule. But now I'm Googling around, and Wikipedia only says that it used to be a rule, and the discussion page says that books from 1951 mention that it used to be a rule. That was before my time... (http://en.wikipedia.org/wiki?title=Talk:Perpetual_check)
I did a lot of digging around this question when I found out it wasn't a rule. Apparently in only ever really even got referenced in that one version of the rules (1951). I believe the thinking behind its omission is that a perpetual check situation will eventually lead to either 3 fold repetition or 50 moves without a capture or pawn move so explicitly having a rule for it is redundant.