Place the chicken breasts in the bottom of the slow cooker in a single layer.
Top the chicken with the diced onion, pressed garlic, dried oregano, ground cumin, chili powder, and salt.
Open the can of chipotle peppers, remove the peppers, split them and scrape out seeds if you prefer less heat, then add the peppers, the adobo sauce from the can, and the tomato sauce to the slow cooker.
Cover and cook on high for 2.5 to 3.5 hours, or until the chicken is cooked through and tender.
Carefully remove the chicken to a cutting board and shred with two forks or tongs.
Optionally, blend the sauce in the slow cooker with an immersion blender until smooth, then return the shredded chicken to the sauce and stir to combine.
Heat a skillet over high heat and toast each corn tortilla briefly on both sides until it just begins to brown.
Fill each tortilla with the shredded chicken, then top with shredded romaine, pico de gallo, and crumbled cotija cheese. Serve immediately.
