Chip:
There used to be a few more of them in Scotland, before they started tacking extra tees onto such holes, particularly at St. Andrews. I think the 12th on The Old Course still weighs in under 330, though.
Tom:
The Links Trust website lists the 12th at the Old Course at 316 (although that's to an overall length @ 6,721, much less than the Open set-up. I don't know that the R & A allows play on TOC from the tournament tees for daily play.)
Machrinahish has done exactly this -- the 6th (Balaclava) played for years as a 315 yd (from the tips) par 4 with an incredibly awkward tee shot, to a neat semi-punchbowl green fronted by two little pot bunkers. It's since been extended to 348 with new tees. The 18th at Machrihanish plays to 314, but it's the least distinguished hole on the course.
Others in Scotland:
Boat of Garten has several very good short par 4s; those under 330 include: the 10th, 271, a very good gambling par 4 that turns to the left, with a very sharp fall-off to the left in the rough, and a green that's only 25 yards deep fronted by two bunkers; the 14th, Spey, with an elevated tee alongside the rushing Spey River to a doglegging right fairway that's very tough to hold, and a very shallow green again fronted by two bunkers; and the fun 16th, Gully, 307 yards with a major depression some 200 yards from the tee. You can play short of the depression and leave a 7-iron or so to the green over the depression, play into the depression and have a totally blind 110-yd shot into the green, or try to carry the depression and leave a short pitch. A neat little bunkerless hole.
Crail Balcomie has three very fun short par 4s: the opening hole (321), a very sharp downhill tee shot with fairway bunkers right, mounding in front of the green, and a funky, L-shaped green that is quite shallow or quite narrow, depending on where the pin is placed; the 9th, a blind tee shot because most of the fairway and green lies below a ridge about 150 yards from the tee. The tee shot is made all the more awkward because of an ancient stone wall that runs alongside the right of the fairway and angles into the line of play, and features a deep but narrow green with several bunkers left; and the 15th, right alongside the sea, a gently doglegging right hole of 266 yds where the golfer has to fit a tee shot in between the beach left and several fairway bunkers right. Those steering away from the large and deep greenside bunker right will find a green that shrugs off shots left; a simple hole if played as a long-iron/pitch, but fun for those trying to drive the green.
Fraserburgh has a terrific 328 yd par 4, the 4th (Shelf), where a fairly simple tee shot leaves an exacting and tough uphill pitch to a small green with severe fall-offs all around; it plays as #3 in the stroke index of the course, a rarity perhaps for such a short hole.
Peterhead's 17th (316 yds) is quite fun, part of the course's very good back nine, with a tee set high in the dunes, at a diagonal to the fairway, and a tiny green set amid a smaller set of dunes.
The obscure and remote 9-hole Traigh on the western coast has two terrific short par 4s: #4, Jimmy's Choice, 257 yds, slightly doglegging right hole with a tee shot over a ridge to a green unseen from the tee; and #6, McEachen's Leap, 283 yds, doglegging left around junk and over the same ridgeline to a green tucked into a small dell-like setting.
The cult-ish Stonehaven, a Braid near Aberdeen, starts off with a 305 yd par 4, with a tee hard by the clubhouse, downhill straight out to the North Sea, with Hitler's Bunker awaiting tee shots tugged left, and a green that seems perched on the cliff's edge.