Making tamales is labor-intensive, but that's what it's about: The love you put into it really comes out in the tastiness of the end result.
Put 12 corn husks in a large bowl, cover with hot water, and weight down with a plate to keep them submerged. Soak until soft and pliable, about 2 hours; drain.
Simmer chicken in broth 12 to 15 minutes. When cool enough to handle, shred into small pieces.
Combine masa harina, lard, and salt in a food processor and pulse until the consistency of coarse cornmeal. Transfer to a large bowl. Add 2 cups corn to processor and puree; transfer to bowl with masa mixture. Stir in remaining cup corn and warm broth. Knead mixture with your hands until a dough forms. Cover with a damp towel until ready to use.
Tear remaining 3 corn husks into 24 thin strips. Season chicken with salt and pepper. Place 1 soaked corn husk on your flattened palm. Pinch off 1/3 cup dough with your other hand and press it into center of husk to form a 4-by-3-inch rectangle. Press 1/4 cup chicken into center of dough. Close your palm so sides of husk cover filling, and place on a work surface with a long side of the husk facing you. Roll up husk into a tight log, fold over the wider end of the husk, and tie with a strip of corn husk. Twist thinner end of husk and tie with another corn-husk strip. Repeat process to form remaining 11 tamales.
Insert a steamer basket inside a large pot filled with 1 inch of water and bring to a boil. Place tamales in basket, cover, and steam 1 hour, checking pot occasionally and adding hot water as needed to prevent scorching. Serve tamales with salsa.