I think China's R&D in "Carrier Killer Missiles" is probably more likely to do it:
http://en.wikipedia.org/wiki/Close-in_weapon_system
The CIWS is only used if the SeaSparrow missiles (which have a 40+ mile range) and RAMs do not hit their target.
http://en.wikipedia.org/wiki/ESSM
http://en.wikipedia.org/wiki/RIM-116_Rolling_Airframe_Missil...
Those would only be used if the jamming equipment/planes failed.
Don't forget that carriers always have several ships traveling with them with even more anti-missile firepower.
It would literally take a nuclear missile, severe incompetence, or numerous malfunctions on multiple well-tested systems to hit an aircraft carrier with a missile. Plus balls, the US will come after you hard if you mess with one of it's carriers.
But yeah, shooting a missile with multiple nuclear warheads is about the only thing that can be done to take out a carrier, and that's a pretty awesome claim.
Oh, I guess a railgun would work too, those would be the real carrier killers. The US DoD should definitely assign some extra IT security personnel to the contractors working on railguns.
Also, what happens if China fires, say, a few dozen of those missiles at once at a carrier group? After all, those missiles are a hell of a lot cheaper than a carrier.
America fields the world's largest number of carrier task force in the world. The other Western countries have maybe one each. Apparently, it required not only technical skills, but also a certain culture and discipline of the crew manning the carriers. As such, the Soviets were unable field effective carrier task force and ended up building a submarine fleet instead.
With the Soviets gone, that left the US Navy as the undisputed power on the high seas, at least, if you are going by numbers of carrier task force. It's the primary offensive power of the US Navy.
... and if there is technology that renders it obsolete, it would be a major concern.
Note, in my original post, I was not talking just about carriers. I was talking about entire carrier task forces, where escort ships (like the cruisers fielding Aegis) are centered around the single carrier.
I have not looked at this in depth. Apparently, carriers are costly to produce and requires a significant technical skills and discipline among the crew. A drone carrier that can pack the same offensive capability, yet doesn't require the level of skilled and disciplined crew, and is cheaper, is significant. Particularly, combined with the "carrier killer missiles".