Consider the following argument:

1. Love involves appreciation.
2. Appreciation of something is irrational if it has no value.
3. It is rational to love other persons.

Now, I suppose value comes in different forms, and what we really need is objective intrinsic value. Well, people usually don’t love other people because of what they can do for them (extrinsic value). After all, to appreciate another person as simply a means isn’t really loving them, is it? So, we have the following:

4. Love for other persons involves appreciation of their intrinsic value.

From which it follows that,

5. Therefore, other persons have intrinsic value.

UPDATE (03-09-2013): after a brief discussion, it seems that this argument doesn’t work. For one, assuming that in (2), (3), and (4) we are speaking about objective value (which is needed for the conclusion I was looking for), (2) is false: it is perfectly rational to appreciate something that has merely subjective value to the person doing the appreciation.