In the majority of US states you can order free-T3 testing online and have the blood drawn at a local blood draw center (see my general overview of the process).
The most commonly-suggested measure of T3 is free T3. See the next section if you want total T3.
I'd suggest ordering from Life Extension because they have the cheapest price I know of ($31), and I've been happy with their service. You can also compare the other 5 free-T3 test providers I've found.
Take a look at my state-specific issues page if you're in AZ, MD, NJ, NY or RI.
Smart-dude Ray Peat disagrees with the common view of what free-T3 testing indicates and suggests total-T3 testing instead. So here are the total-T3 providers I've found: