I'm with subfixer. I can't claim to have lived my life surrounded by anchor chains, but of the fair number I've seen (excluding pre-twentieth-century ones) virtually all have been studded.
The studs, incidentally, don't contribute anything to the strength of the chain. (The stud generally is slightly smaller in cross-section than the material used for the link itself. When stress comes on the chain, none of it comes on the stud.) The purpose of the stud is to help prevent the chain from getting kinked up in the chain locker. You'll rarely, if ever, see stud-link chain used in any other application than for anchor chains. The chain bowsprit rigging of nineteenth- and early-twentieth-century ships like the Cutty Sark, for instance, was normally made of ordinary, oval-link chain.
In his books on sailing ship modeling the late Harold Underhill described a method for making stud-link chain. (He had, as he freely admitted, a bit of an obsession with making every part of his models himself.) He started out by bending a bunch of pieces of brass wire into tight S shapes, then hooked them together and laid the resulting "chain" on an asbestos block. Then he'd silver-solder the gaps in the S shapes together. The photos of Underhill's work make it clear that his chain looked pretty daggone good. But he, of course, was working on relatively large scales - generally 1'8" = 1'.
To be honest, I can't recall ever having seen a set of anchor chains on a 1/350 or 1/700 model that I found really convincing. The molded-in ones provided by the kit manufacturers have obvious drawbacks (though the better ones do depict the studs). I've tried the photo-etched metal ones from Gold Medal Models; they always look to me like strips of thin metal with holes in them (which is what they are). Fine, unstudded chain is probably ok for the relatively small stuff on such ships as destroyers, in which the studs probably wouldn't be visible to a post-middle-aged set of eyes like mine anyway. But on 1/700 battleships, and 1/350 subjects of all sorts, it seems to me that unstudded metal chain isn't really much of an improvement over the molded-in versions.
I've heard that, with patience, it's possible to find stud-link chain at some jewelry dealers. I confess I've never really had occasion to look for it - and I'm inclined to doubt that a jeweler would carry it in sizes small enough for 1/350 models. I don't really have a solution to the problem.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.