Khelavaster is the sage who discovered the Coming of Chaos, and entered the dungeons hoping to stop it, but never returned. You'll meet him somewhere below the Animated Forest and the Dwarven Halls, usually on D:16. Unfortunately, he will be mortally wounded when you find him, and the only (known) way of saving him is to give him an amulet of life saving. (N.B. Talking to him will allow him to die.) He is also on the down staircase, and it does not seem possible to get past him without either saving him or letting him die.
If you save him, he'll give you a very nice reward including six blessed scrolls of chaos resistance, and if you're attempting an ultra ending, saving him is compulsory so that he can summon the Trident of the Red Rooster. Therefore, most people will try to save him if they can, and will wish for an amulet of life saving for him if they get the chance. Extreme chaotics who feel that saving him is out of character can always kill him after he reappears in Terinyo. See Andy Williams' Guidebook for a bit more detail on Khelavaster.
If you are lucky enough to acquire an amulet of life saving before you meet Khelavaster, take great care of it. I'd recommend that you stash it somewhere safe (such as the Old Barbarian's Glade) at the first opportunity and do not pick it up again until you're ready to give it to him. If you keep it with you, and especially if you wear it, you run the risk of having it destroyed by a trap, which is extremely annoying.
If you haven't found an amulet of life saving by the time you meet him, don't give up yet. There is no time limit on saving him - you can head off and spend months searching for the amulet, and he will still be alive when you come back. Here's a list of strategies you can employ in the attempt to find an amulet of life saving:
It may help your search to know that ordinary rings are often (not always) rings of djinni summoning.
Potions of exchange are quite rare, but there is no risk involved in dipping items into them, and if you dip a heap of 19 useless rings you may get a heap of 19 rings of djinni summoning out of it. Potions of raw chaos can be manufactured by dipping a corrupting artifact such as Moon Sickle into useless potions.
N.B. Playing chaos roulette is very risky. The potion may explode, doing 100-200 HP of damage and causing about four corruptions. To reduce the risk, do all of the following before you start:
Items transformed by chaos roulette will always come out cursed, and if you dip a heap of 19 useless rings into a potion of raw chaos you'll only get one ring out.
If you've tried everything and you still can't find an amulet of life saving, you might hope for some way to avoid allowing Khelavaster to die, or failing that, to wish him back from the dead when you finally get a wish. For example, the first time I got a wizard that far, I thought ``No problem - I'll just teleport him out of the way and go on,'' but it did not work because he resisted my teleportation spells. Here is a list of all the alternative strategies I've tried or heard about, none of which actually work.
If only you could move Khelavaster off the down staircase, you could explore the deeper levels of the Caverns of Chaos. You'd be practically certain to find an amulet of life saving or some way of wishing for one down there (because of the high danger level), and then you could come back and save him.
It would be nice if you could call Khelavaster back from the dead with a wish, but you can't. Wishing for ``Khelavaster'' silently fails, and wishing for ``ancient sage'' results in ``Nothing happens''. I've heard that wishing for ``dying sage'', ``Khelavaster, the ancient sage'', or ``Khelavaster, the dying sage'' will all also fail.
Many thanks to David Chapman, Vladimir Panteleev and several people on the ADOM forums, including Dougy, Messiah, Jan Erik, Locke and HicPotboy, for some of the information in this spoiler.