In a small bowl, combine the paprika, chili powder, cayenne, cumin, sugar, and 1/4 teaspoon of the salt.
In a large saucepan, heat 2 tablespoons of the oil over moderately low heat. Add the flour and cook, whisking, until golden, about 3 minutes. Add the garlic; cook for 30 seconds. Add the paprika and chili powder mixture and then add the broth slowly, whisking, until smooth. Bring to a simmer. Simmer, covered, until thick enough to coat a spoon, about 25 minutes.
Meanwhile, in a large frying pan, heat the remaining 1 tablespoon oil over moderate heat. Season the chicken with the remaining 1/4 teaspoon salt and the pepper and cook until browned and just done, about 5 minutes per side. Remove the chicken from the pan and let it rest for 5 minutes. Cut crosswise into slices.
Add the tortilla chips to the chile sauce and cook, stirring, until the chips are soft but not falling apart, about 2 minutes. Put the sauce on plates and top with the feta, sour cream, onion, cilantro, and chicken.
Wine Recommendation: These forceful, varied flavors need a gutsy wine, and zinfandel will more than hold its own. Look for old-vine cuvées from Sonoma's Dry Creek or Russian River valleys.