AudioGuru,
Actually, we are both wrong. Here is the snip taken directly from the OP's posted data sheet:
There is no requirement that R1 be 120 or 240 Ohms; only that if it is higher, like the op's 1K, then he shouldn't be surprised if the voltage rises if the load is removed from the output of the LM317. In some battery powered applications where battery life is important, and when the minimum load spec is otherwise met, it is not necessary to have such a low value for R1.
Show me on the data sheet where it says to use a 120 Ohm resistor for R1. I just read todays version of the data sheet, and couldn't find it.