I read somewhere (maybe allpar.com) that the DOHC Hemi was a response to the Ford 427 SOHC "Cammer", when this engine was forbidded in NASCAR, Moper stopped the development of the DOHC Hemi.
Dual overhead cam HemiA 426 dual-overhead cam Hemi was actually produced - two of them, in fact, and both were made in 1964. The DOHC Hemis were made to counter Ford's response to the 1964 426 Hemi, the 427 SOHC, but when NASCAR ruled against Ford's engine, there was no need for the overhead-cam Hemi.
Neither of the DOHC Hemis were ever placed in a car; one was destroyed, the other moved to the Kansas City area. (source: Muscle Car Review. Thanks, Stéphanie Dumas.) Recently, famed engine builder Larry Shepard told us that he has the A-925 cylinder head and other related parts, purchased from the late Dan Napp.
An article by Tom Shaw in Mopar Muscle went into more detail. The DOHC Hemi was project A-925, and it would need to be much more powerful than Ford's SOHC 427, but still rugged enough for racing - and able to conform to NASCAR's rules. Two possibilities were considered, according to Shaw - one using two cams positioned between the heads, in the "valley;" four valves on each cylinder were operated by lifters, pushrods, and lifters. This expensive setup was an unused contingency plan. Nearly as ambitious was an engine with aluminum heads, dual overhead cams, and, again, four valves per cylinder, with pent-roof chambers. (Chrysler had been working with four valve per cylinder engines for a never-completed Indy run in 1963.)
The dual-plane intake manifold had eight runners per side (Chrysler was into efficient and innovative intakes) and made of magnesium - but designed for a single four-barrel carburetor, as required by NASCAR.
The cams were driven by a cog belt, using external cog wheels at the front of the heads. Because the cams were directly above the valves, valvetrain mass was low, so the engine could rev high - a 7,000 rpm redline was specified, high for the era.
Shaw wrote that no DOHC Hemi ran under its own power; they were driven by an electric motor to check the valvegear. Research stopped in 1964 when NASCAR banned the SOHC 427 and Chrysler's own race Hemi. One DOHC Hemi still exists.
DOHC Hemi Update: Jon Field wrote that there was a third (at least) DOHC Hemi made — and that he owns it, a 301 cid aluminum-block-and-head engine with twin cams, two cam covers on each head (the plugs are between them), hydraulic tappets, brass valve seats, and four Weber two-barrel carbs (165 cfm each). He says the oil pan holds 10.6 quarts, and that the engine has stainless steel headers, and an aluminum intake; it is apparently functional and runs on regular gas. We don't have any information on where it came from and whether it's a Chrysler effort or an aftermarket modification.
Here's a pic someone made in 1/24 scale for a '70 Super Bee model: