Hey, so one of my PCs is a Droid Explorer (Archeologist) that has most of his obligation as sort of an obsession/addiction that basically amounts to kleptomania. Which for an archeologist droid that may have some faulty parts, is entirely feasible.

However, I have no idea how to deal with the narratively when the PC's obligation is rolled or how to keep it rolling outside of that as well.

Any ideas/suggestions?

This sounds like the player is going to want to be constantly stealing things, which may be a pain for the other players, depending on how he goes about it. You may want to talk with the player a bit to make sure he's not planning on having his character screw with everyone else's, because that will likely not lead to a very fun time.

As for what you can do when obligation is rolled, have the consequences of the player's theft come to bite him. He meets someone he stole from. Their ship is carrying some very hot contraband he grabbed off someone. Things like that.

First of all I have to ask: is his obligation directed towards archaeological artefacts, or is he a more general kleptomaniac? If the latter I'd let the player know in advance that stealing from other characters should not be done, since it tends to create considerable irritation around the table. It would probably be more fun, as a GM, to wait until his obligation comes up and then place him in a position where there's lots of stuff he'd want to steal but it would have interesting (not necessarily unpleasant) consequences to do so. And maybe have him make some Discipline checks to keep his sticky fingers to himself when it could otherwise cause trouble.

When his obligation comes up a double I'd have his past misdeeds show up to haunt him. Perhaps he stole something once from someone who wants it back very badly and sent some rough people to repossess it. Or maybe something he stole turns out to be more important than first imagines, and now lots of people are after it - and they all know it was last seen in your player's possession. That sort of thing.

And if you want an idea for how to reduce his obligation, you could create an adventure around him having to return such an item to its rightful owners, be it a museum, a private collector or some ancient civillization looking for their idol.

I never heard this on an episode of the Order 66 Podcast but they recounted a session that a GM ran with a kleptomaniac (addiction obligation) PC—he would ask the player to make Skulduggery checks at random to represent the uncontrollable behavior.

Success would mean you aren't noticed. Failure means you get caught. Advantage means you got something valuable. Threat means someone eventually notices that the item is missing and starts investigating. Triumph means you stole something awesome or unexpectedly useful like a monkey paw that grants wishes! That's good! Despair means that monkey paw artifact twists your wishes and grants only disappointment. That's bad.

Ugh, never let someone play a Kender.