For the grilled chicken: Preheat a grill to 300 degrees F, then reduce the heat to 200 degrees F.
Chop the chicken thighs and add to a bowl. Add the lime juice and season with salt and pepper. There is no need to marinate, just put the chicken straight on the grill and cook until golden but not too dry, about 20 minutes. Set aside for the sope assembly.
For the sope: Mix the Maseca with 1/2 cup water in a bowl and mix by hand, adding more water if necessary, until you get a putty-like consistency. Using your hands, shape the Maseca into circles about 1/4 inch thick and 4 inches wide. Place the sopes in a non-stick pan and cook until light brown, 1 to 2 minutes per side. While the sopes are warm, pinch the top side up to create an edge all the way around. Let them cool for 30 minutes.
Pour the enchilada sauce into a bowl and dip the sopes in the sauce, completely covering them. Let the sopes sit for 30 minutes at room temperature.
Fry the sopes in a deep-fryer or pan filled with enough canola oil to cover them for 2 to 3 minutes on each side, or a little longer if you want them crispy. Put 1 sope on each serving plate and top with the grilled chicken, refried beans, queso fresco and iceberg lettuce divided evenly among the 4 plates. Garnish with the radishes, jalapenos and tomatillo salsa and serve.
Maseca is an instant corn masa flour made of 100% corn. It can be found in specialty Latin grocery stores.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.