Where is oxygen sensor bank one THREE on 1997 Chevy blazer?

On a 1997 Chevy Blazer, "bank 1 sensor 3" refers to the third oxygen sensor on the engine bank containing cylinder #1. Since it's a sensor 3, it's likely located after the catalytic converter.

Precise location varies slightly depending on the engine (4.3L, 5.7L, etc.). You'll need to consult a repair manual specific to your Blazer's engine. A Haynes or Chilton manual, or an online repair database (like AllDataDIY), will have diagrams showing the exact location. Looking up your VIN can also help in finding the right diagrams.

Without knowing the exact engine, I cannot give a more precise location. However, the general area to look for it is downstream (after) the catalytic converter on the exhaust manifold side of the bank containing cylinder #1.