Why is coolant coming out of the timing chain case

Any where back there is a head gasket leak, unless it is at the very front of the engine(passenger side). Then it could be the timing chain cover. Use a mirror and bright light, You can find it.

Yes the timing cover gasket can leak coolant. The coolant passes the waterpump and is pump into the engine block thru the timing cover. to see the actual leak jack up passenger side of car support with jack stand take off wheel and the splash guard now you can see the crank shaft pulley look up at waterpump on both side it goes back to engine block with a mirror you can see it leak.

Water pump is going out.

There is a compression tester for the radiator. It is a special cap that fits on and you pump it up. This will allow you to look for the leak with the engine cold and not running.

probably a gasket that seals coolant behind cover. I don't remember if there is a freeze plug there.
sometimes a head gasket leak can do the same but not very common.

Tale the truck to a shop and have the cooling system pressurized to see where the coolant is coming from is my advice. They do leak at the heater hose above the passenger side rear most cylinder, remember water is clear and coolant is green or yellow or reddish colored and feels slimy to the touch, water is of course clear..

CHECK FOR LEAKING WATER PUMP WEEP HOLE OR GASKET.ALSO CHECK WATER PUMP HOSE FOR LEAKS.IF ALL LOOKS GOOD.YOU COULD HAVE PINHOLE LEAKS IN RADIATOR CORE LEAKING ON FRONT OF ENGINE OR INTAKE MANIFOLD GASKET LEAKING COOLANT.

the leak is most likely your waterpump get another mechanic's opinion to be sure; the chain does not need to be touched
if it ain't broke...don't fix it

It's on the left side (driver side). It's by the belts. You can't see the water pump from the top side.
If you want to get to the water pump you have to remove the top radiator cross member, the fan assembly, the crank pulley, the timing covers, and the timing belt.

duh...fix the leak!