The factories in China, where most of the mats are made, are heavy on the use of chemicals. The odor penetrates the mats and remains for a long time.
I had to replace my 1990s Fiskars (no odor ever back then) a few years ago and asked on here first for recommendations, and kept reading about the heavy odor. So when I finally decided I wanted an Olfa mat, I ventured to JoAnn and went to the very back mat hanging on the peg. I figured it had been there the longest. I smelled it and it was okay (although I was put off by the ones hanging on the front end. I took off the 7 or 8 in front (must've looked funny to anyone around, but who cares?) --which isn't exactly easy--but then put the mat in my cart, replaced the others on the peg, and drove around the store to test the mat for odor. It was only faint. I brought it home, poured vinegar on it, set ii out in the sunshine for a day or two, and it was fine.
That said, if I had to replace it again, I would certainly look into what yngldy suggested--the Calibre Art ones. Never heard of them, but I trust what I read. It'd be worth the extra money to me, considering you have a mat for a LONG time, so the price difference over years is negligible for the price of your lungs.