To make the marinade, toast morita chiles in hot oil to soften and place in high speed blender. Add all other ingredients except oil and chicken. Puree until smooth. With the motor running, slowly add oil. Check for seasoning. Pour over chicken and marinate, in the refrigerator, for 10 to 12 hours.
To make the salsa, combine all ingredients in a bowl. Check for seasoning and set aside.
To make the tacos, heat a grill to medium-high heat or direct heat cooking. Remove the chicken from marinade and season with salt. Grill chicken until no longer pink in the center. Chop.
Wrap tortillas in foil and add to the grill to warm. Fill the warmed tortillas with diced chicken and drizzle with crema and sriracha. Spoon salsa over top and finish with cilantro. Serve immediately.