How much should it cost to replace the timing chains, 2009 Explorer V6

You have 3 chains to deal with, the main sprocket and a LH and RH 'cassette' to each overhead cam. It's a very involved system, and requires a few special tools. Basically you are disassembling the entire front of the engine. You can either remove the front clip (including AC system) to get access or pull the motor. I'm not familiar enough with this specific vehicle to say if crank sprocket can be removed without interference from crossmember. It's a pretty involved job too, the labor time for the crank to main sprocket is about 5 hours shop time, that doesn't include the two cam chains (aka cassettes) and their sprockets. It's also one of those job where you think 'maybe I should replace head gaskets since everything is apart.' Most mechanics I've ever know really don't like to pull motors if they don't have to, so if it can be done in car they'll find a way. But if you are not comfortable with their estimate, then shop around. Also check a repair guide for your vehicle, it'll give you the skinny on what's involved.

Yes, the engine has to be removed and that just increases the cost of an expensive job. The chains are probably fine, it is the rubbing blocks and tensioners that cause the problem.