The chicken taco is the neglected stepchild of Chicago's taco scene. Unless the restaurant in question is serving chicken grilled over charcoal (like here or here), in which case you usually have to construct the taco yourself, I've found it best to avoid the whole, tasteless genre. The only other exception is if you see "chicken tinga" on the menu, in which case the meat is stewed in a flavorful liquid and pulled apart while still tender.
To see one of the very best examples of this around, make your way to Taqueria Perejil in Logan Square. Perejil leaves the chicken in sizable, juicy pieces, instead of dishing out a tangle of mushy meat. But my favorite part is that in the place of a watery sauce, the taqueria mixes in sliced chipotle slices. Though slightly spicy, they mostly add a robust and earthy note. If you miss the spice, dip into the incredibly hot green salsa on the table.