I'm working my way through my first campaign (SciFi on, Tons of Guns on, IronMan off), and I've been teaching myself about the game with the aid of an online FAQ that I downloaded.
So I recovered the Chalice of Chace from the museum in Balime, and trudged up to San Mona, turning it over to Kingpin for the $20k cash reward. But I then wanted to recover it and give it to Yanni in Chitzena.
My team snuffed Kingpin and all his men in San Mona, but now I can't find the Chalice anywhere. I've turned San Mona upside down, starting with Kingpin's mansion and working outward from there (I figured it would still be on his body, but it wasn't). It's also not in the mine with Kingpin's cash, which seemed another likely hiding place.
Is the Chalice gone forever, or am I missing something obvious?

Did you kill Kingpin right after giving him the Chalice or did you wait?
If you did it rightaway, he should drop it when you kill him.

I think that's the problem--I didn't kill him right after giving him the Chalice (I'd only sent a few of my people up to San Mona to deliver it, and I didn't want to try fighting Kingpin and his men until I'd gotten the rest of the team up there to help).
So I came back to Kingpin's mansion some time later--probably at least a day. I killed every one of Kingpin's troops, and Kingpin himself, but the Chalice is now nowhere to be found. I double-checked Kingpin's body, and it's definitely not there.

Reload an old save game if possible.
Returning the chalice to Chitzena raises loyalty in all city and SAM sectors under your control.