I've long given praise to the chicken offerings at Ino's Tacos, although, I have no aversion to dark meat so my opinion might not be for you - in that I'm not sure how much dark meat is in their mixture. Their chicken is the best I've found. I do, however, think that some dark meat might be included in their mixture, but not enough for me to say for sure. Is all white meat what you are looking for? If so, then two spots might be up your alley:
Zacatacos (various locations)
Las Asadas (Various locations as well)
In my experience with these two, both use only white meat, and do not boil it to death in some oversalty red sauce (huge pet peeve of mine.) Las asadas uses bigger chunks of chicken, while zacatacos is more smaller bite size chunks. Neither "sing" like Ino's does, but both are pretty competent - more so than the average joint. I have also heard that El Asadero up on Montrose is competent as well, but I haven't tried their chicken offerings.
Ino's Tacos (there is another one on one of the 40ish streets somewhere?)
7100 Roosevelt Rd
Oak Park, IL 60304
(708) 763-9571
Zacatacos (various)
Las Asadas:
2072 N Western Ave (and other locations - Including La Palapita up north on Milwaukee)
Chicago, IL 60647
(773) 235-5538
Taqueria El Asadero
2213 W Montrose Ave
Chicago, IL 60618
(773) 583-5563
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