Shredded Chicken and Cheese Taquitos

Place chicken in a single layer in the bottom of a large saucepan. Pour in cool water until chicken is covered by 1 inch. Bring to a boil over medium-high heat. Reduce heat to a simmer, cover, and cook until no longer pink in the center and the juices run clear, 10 to 14 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Transfer chicken to a cutting board and shred meat with 2 forks when cool enough to handle. Discard poaching liquid.

Preheat the oven to 350 degrees F (175 degrees C). Grease a baking sheet.

Heat oil in a large skillet over medium heat; add onion. Cook and stir until the onion has softened and turned translucent, about 5 minutes. Add shredded chicken, olives, chiles, water, and taco seasoning; bring to a boil. Reduce heat to a simmer and cook for 10 minutes. Add Mexican cheese and stir until melted. Remove from heat.

Warm tortillas on a griddle over medium-high heat until soft, about 10 seconds per side. Add chicken filling to each tortilla, roll up tightly, and place seam-side down on the prepared baking sheet.

Bake in the preheated oven until edges are brown, about 30 minutes.