Add diced tomatoes, chipotle peppers, oregano, garlic, salt and onion in a large blender. Blend until smooth.
Heat a large skillet (skillet with high sides) over medium-high heat. Add olive oil and blended tinga sauce. Cook for 10 minutes.
Add shredded chicken and toss with sauce until fully combined. Reduce heat to low and for 10 more minutes, stirring occasionally. The sauce will thicken and reduce a little during this time.
Remove from heat, taste and season with more salt if necessary.
Serve chicken tinga in warm corn tortillas, flour tortillas or lettuce cups. Top with cotija cheese, diced onions and cilantro.