Potential Stupid Question Alert:
Are they really on our level yet?
Saying they have the missile tech to shoot doesn't mean a number of things. You'd have to assume a lot to assume it's combat ready
1. They have launchers capable of shooting it accurately (Russia has alot of problems with that)
2. They have the means to spot our ships in open sea.
A. They have the means to keep that target track relevant enough to point and shoot the missile.
3. They have the political will to withstand the massive retaliation consisting of what would still be 11 aircraft carriers, ICBMs, Long Range Bombers, etc etc etc etc
Given all those assumptions and then some, isn't it safe to say we've not got that much to worry about yet?
There are a lot of people geting paid a lot of money to figure all that out...and they don't have any idea, either. Personally, I doubt the Chinese really know the answers, either.
One thing is for sure - the Chinese aren't as doctrine-bound as the Soviets were. They study our weapons and tactics very closely and are willing to flex and adapt.