If the oil pressure light comes no, it means the oil level is so low, that when running, sometimes there isn't enough oil in the pan for the oil pump to pickup... thus causing low oil pressure.
When this happens, things that need oil badly, like your timing chain, do not get oiled. It is possible, and likely, the reason you need a timing chain kit, is because of the oil problem. Which means if you fix the timing chain, and not the oil issue, you will likely screw up the new timing chain too.
I am assuming that you have properly checked the oil level, and can clearly see that it is too low after 2K to 3K miles of driving.
So issue now is, where is the oil going. Oil normally goes in one of two spots... It's leaking, or it's being burned.
If it is leaking, you should see either a puddle of oil on the ground after your car has sat there a bit, or you should see oil covering parts of the engine where it leaked out.
If it's being burned, you should see dark smoke when you first start the car up, or a slight smell to the exhaust when it's running.
If it isn't leaking... and you can't see any indication that it's burning oil... then (honestly) sell the car. It means you are losing oil internally, and that means a bigger issue, and requires a full engine rebuild to fix. That's a lot of money, and IMO, not worth it.