Since I don't want to buy spinning fibre by mail and wind up with fibre that has a chemical smell to it again, I asked a shop owner to tell me about some fibre she offers.
She phoned her supplier and found their product meets Oeko-tex® standards.
This was the first time I'd heard of Oeko-Tex®. According to the site, Oeko-Tex® does tests for "textile products of all types which pose no risk whatsoever to health." Their tagline is "Confidence in Textiles."
Sounds good to me.
Got a sample. There's a faint smell that might be processing oil.