Translation:He eats chicken even though he does not eat fish.
A little off topic, but of potential interest for other learners...
I was looking for Italian songs to listen to/translate while I learn. I found this one the other day by Annalisa that features several "anche se" sentences ("Potrei Abituarmi"): https://youtu.be/vFWE-BFovOg
Here are the lyrics: http://www.metrolyrics.com/potrei-abituarmi-lyrics-annalisa.html
It is also catchy, if I do say so myself.