Broil whole poblanos on a rimmed sheet about 6 inches from the element, turning until blistered, 10–15 minutes. Cover in a heatproof bowl for 10 minutes. Peel when cool enough, remove stems, seeds, and pale ribs, then cut into strips about ¼ inch wide. Begin the chicken while the peppers steam.
Pat chicken dry and season with ½ teaspoon salt and the pepper. Heat oil in a large skillet over medium-high heat. Brown chicken in two batches for about 3 minutes per batch, turning once; it will finish cooking later. Transfer to a plate.
Reduce heat to medium and melt butter in the skillet. Cook onion for about 5 minutes, scraping up browned bits. Stir in garlic and oregano for 30 seconds. Add corn, poblano strips, broth, and remaining ¼ teaspoon salt.
Return chicken and any plate juices to the skillet. Bring to a gentle simmer, cover, and cook for 5–7 minutes, stirring once, until the thickest chicken pieces reach 165°F. If the pan becomes dry, add a small splash of broth.
Turn heat to low. Stir a few spoonfuls of warm pan liquid into the crema, then gently stir the tempered crema into the skillet. Warm for 1–2 minutes without boiling. Remove from heat and stir in lime juice. Taste and adjust salt.
Serve with warm tortillas or cooked rice, spooning the onion, corn, and sauce over each portion. The sauce should move freely around the chicken; loosen it with a spoonful of broth if needed.