2001 chevy silverado 5.3 ltr I am adding 1 gallon of antifreeze between oil changes. I am not seeing any in the oil, and it not leaking. Where is it going?

This is one that you will need to do some careful looking to find. every hose connection needs to be looked at for damp residue as well as all gasket parting lines (thermostat housing, head to block parting lines, intake manifold ends etc.) You may also need to have a shop to a radiator pressure test as well as a cylinder leakdown test (which will pick up on most internal leaks) If seepage is very minor, coolant can burn off or boil out before reaching a noticeable level inside the engine or even at a gasket to the outside. A small crack between the valves in a cylinder head can be so small that it goes unnoticed when exiting along with exhaust. A small leak now may be difficult to find but locating it now is better than waiting for a larger failure. It may turn out to be something simple as a bad cap on the radiator or the shaft seal beginning to fail on your water pump...letting it go can eventually cost you an engine.

I have a chey suburban 2004 with 5.3 and had a coolant leak that i could not find. i found out that chevy is having problems with Castech cylinders heads leaking coolant around valve seats.Chevy recommends to replace the heads if this is the problem but i fixed mine with high quality coolant leak additive(about $40 a bottle) this was done about 30,000 miles ago,it now has 165,000 miles.Do some searching about Castech heads and follow procedure to determine if this is the problem or not.

On your bottle you have cold and hot marks,DO NOT over fill your bottle when it's cold it will only come out of the over flow when you drive.it will just go to waste.