Season the chicken thighs on both sides using about ½ teaspoon kosher salt and ¼ teaspoon pepper. Heat the olive oil in a large Dutch oven or deep skillet over MEDIUM-HIGH heat. Add the chicken thighs, in batches, if needed, and cook for 2 to 3 minutes per side, just until lightly browned. Transfer to a plate.
Reduce the heat to MEDIUM. Add the sliced onion to the pot and cook, stirring occasionally, for 5 to 6 minutes, until softened and lightly golden. Add the garlic and cook for 30 seconds more.
Stir in the fire-roasted tomatoes, chicken broth, chipotle peppers, adobo sauce, oregano, cumin, bay leaf, salt, and pepper, scraping the bottom of the pot to loosen any browned bits.
Return the chicken to the pot and bring the sauce to a low simmer. Cover and cook for 40 to 45 minutes, or until the chicken is cooked through and tender enough to shred. Transfer the chicken to a cutting board and shred with two forks.
Remove and discard the bay leaf from the pot. Use an immersion blender to blend the sauce until mostly smooth, leaving just a little texture. Alternatively, carefully transfer the sauce to a blender and pulse briefly.
Return the sauce to a simmer over MEDIUM heat and cook for 10 minutes, stirring occasionally, until slightly thickened and concentrated.
Return the shredded chicken to the pot and stir to coat well. Simmer for another 2 to 3 minutes, until warmed through. Stir in the lime juice and adjust seasoning with additional salt, if needed.