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I'm not sure what "chip" you're referring to, but if all you're doing is installing a different thermostat, yea, you can do it yourself. A stat is just a mechanical device that opens and closes based on the temp of the coolant the spring senses.
It's easy, just a couple of precautions.
The thermostat housing on the 86 Vette is aluminum and cracks easily when torqued back in place. Take your time, use the correct torque value and pull down the bolts in alternating amounts in small increments.
Run them down til they are both flush, then torque them a little at a time. I don't my service manual here or I'd post the torque value, but if I remember correctly, it's pretty low.
If you crack yours, and you'll know when you hear a 'pop' sound, Pep Boys sells a cast iron replacement for around $10; they have them in stock behind the parts counter at the back of the store. They'll crack too, but are just harder to break.
To get the advantage of a lower temp stat, you need to have the fan come on at a lower than stock temp. Modifying the PROM is the best way to do this, but some companies sell a sensor that you screw in the head that is supposed to cause the fan to come on sooner too.
I'm going to hope that someone that knows for sure will jump in, but I think your mileage will drop if you lower the engine temp without changing the PROM.