Step 1Season the chicken breasts with salt and pepper and put them in a shallow bowl. Add the oil, lime juice, shiitakes and chives and mix well. Marinate at room temperature for 30 minutes, stirring occasionally.
Step 2In a large bowl, soak the corn husks in very hot water until they are pliable, about 15 minutes. Heat a grill until very hot.
Step 3Drain the corn husks and wipe them dry. Lay 3 to 4 out on a work surface so that they overlap. With a brush, lightly oil the insides of the husks. Place 1 chicken breast in the center. Repeat with the remaining breasts. Divide the mushroom mixture over the 4 chicken breasts. Season with more salt and pepper to taste. Fold the husks over and up to make tidy packages. (Tie them with thin strips of the remaining husks, or use string.)
Step 4Lay the packets seam side down onto the grill and cook 7 to 8 minutes on each side. Serve in the charred husks with a wedge of lime.