Remove some skin from chicken, if desired (leave some on if you want a crunchy taste). Arrange chicken pieces in a 13x9x2-inch baking pan lined with foil, skin side up. Generously salt and pepper the chicken.
Bake, uncovered, in a 400 degree F oven for 20 minutes. Turn the chicken pieces over.
Meanwhile, stir together the yogurt, apricot jam, cumin, and fresh basil. Spoon 1/2 yogurt mixture over chicken. Bake for 15 minutes.
Drain more fat off, flip the chicken back over (skin side up), spoon the rest of the mixture over the chicken, and bake for an additional 15 minutes. Let chicken rest for 5-10 minutes; serve!