So I've got these large crab-like creatures living on the Abyssal Plain under the ocean (way way down 9800-20,000 feet down). At this depth the main food source is the marine snow, "a slow drift of mucus, fecal pellets, and body parts—that sinks down from the surface waters". And, of course, your neighbors.
Let's call our creatures Crabites for now, because that's their name, and besides, it's fun to say. Crabites.
The Crabites have evolved intelligence and would like to build a civilization. The problem I'm seeing for them is that for civilization you need surplus, which is mighty thin down there on the Abyssal Plain.
The marine snow is not constant; there is a constant rate, but there are huge irregular windfalls (good article: http://www.mbari.org/feast-and-famine-on-the-abyssal-plain/ ). I'm planning to have their lives revolve around gathering and accumulating the regular snowfall, and then snap into frenzied action to gather and hoard as much of the windfalls as possible.
Problem is ... I'm not sure this is enough. I'd like to have some kind of agriculture because of its insane ROI (100 kernels of wheat from one seed, minus slippage). But what can they grow? The best I can think of is shallow-sea hunting, where they float themselves up to the rich zones and kill everything in sight, bringing it down. But -- and here's the main question -- is there anything down that far which can substitute for agriculture?
Update ... I'm seeing some great ideas in answers, in particular harvesting from hydrothermal vents. I am thinking this is promising, as are methane "cold seeps" (https://en.wikipedia.org/wiki/Cold_seep) which are less extreme, can be found in shallower waters, and can support chemotrophic-based ecosystems.
I may have to bump up my planet's volcanism and overall methane production...