Jacobsen Series 7 chair - Bucciarelli Italy?  

For $2, it's a good buy, but no, it is not authentic. This chair was widely copied back in the day up to present times so what you need to do is start from the assumption that it's a fake and prove that rather than trying to convince yourself that it's real. In doing the latter, it's easy to miss subtle differences.
If you compare your photos to those of an authentic chair from on an authorized dealer's site, you can see the differences. You're lucky in this case because one of your photos was taken from the exact angle as a photo on the DWR site. From this you can see that the back on yours is narrower at the top by a little bit and is straight along the sides whereas the real one has a slight curve to the sides. The curve of the seat kind of flattens out at the sides and it's wider than the seat on the real one. The legs seem to be a different distance apart, too.
Still, for $2, who cares! I like the color a lot. And an older chair made in Italy has got to be better than a new one made in China!

Spanky, thanks very much for such a detailed and thoughtful response.
The yellow adds a nice pop of color to our room, and I find the chair a little more comfortable than our plastic Eames chairs. It's a keeper.