Does the Subaru Ascent have a timing belt or chain?

Your Subaru Ascent most likely has a timing chain rather than a timing belt, though without knowing which year specifically You're interested in, I'm not going to say that with complete certainty. Timing chains are actually pretty superior to belts; You don't see them exclusively because they cost more for the manufacturer, and don't generate as much revenue in service charges like belts do. Given proper care, Your chain should last at least 100k miles, and past that; You'll often see the tensioner or other engine components fail long before You see the chain itself die. On the other hand, when a timing chain does go, it can result in some pretty spectacular destruction under Your hood, so make sure You at least give it a looking over now and then.