Preheat a large skillet over medium heat. Add the oil, followed by the chopped onions, peppers, celery, and garlic. Sauté for 3-5 minutes to soften.: As the skillet warms the olive oil will shimmer slightly, and the first sizzle when the vegetables hit the pan is a satisfying cue. You should smell the onion turning sweet and the garlic releasing a warm, nutty aroma within a minute or two. Visually, the onion edges will go translucent and the red pepper will slightly soften and develop glossy surfaces, while the celery will begin to lose its raw stiffness. This quick sweat unlocks sugars and mellows pungency, which helps the slow cooker avoid a raw tasting base. A common mistake is using heat that is too high, which causes the garlic to brown and produce bitterness. Keep the pan at medium, stir frequently, and aim for gentle softening rather than color change.
Pour the sautéed veggies and the drained kidney beans in a large slow cooker. Place the chicken over the top, then sprinkle the chili powder, cumin, and salt in the slow cooker.: When you empty the skillet into the slow cooker you will notice the aroma already building, a warm mix of sweet peppers and spices. Layering the chicken on top helps shield it from direct contact with the ceramic early on, allowing juices to collect and mingle around the meat. Sprinkling the chili powder and cumin now lets the spices mingle with the hot veggies and beans, forming the backbone of flavor. The salt invites those notes to pop. Be cautious about over seasoning at this point, since the long cook concentrates flavors slightly. A common oversight is dumping all spices unevenly; try to distribute them across the surface for balanced seasoning.
Pour the jarred roasted red peppers and their juices in a blender. Puree until very smooth. Pour the pureed red pepper and chicken broth in the slow cooker. Cover and turn on low for 6-8 hours, or high for 3-4 hours.: In the blender the roasted pepper puree will turn vivid and silky, and the scent will be smoky and bright. Blending the peppers with their juices prevents a grainy texture and ensures the flavor disperses evenly. Adding the chicken broth thins the puree into a sauce that will both infuse the chicken and hydrate the beans. Choosing low heat for 6 to 8 hours yields the most tender, melt in your mouth chicken and allows spices to bloom slowly. The high setting is fine when you are short on time but expect a slightly less integrated texture. A typical mistake is skipping pureeing, which leaves chunks that can create uneven pockets of flavor. Make the puree smooth and taste a small spoonful so you can adjust seasoning before the long cook.
When the chicken is cooked through. Remove it with tongs, and shred the chicken with a fork. Stir the shredded chicken back into the crockpot. Serve warm!: You will know the chicken is done when the internal pieces are opaque and tender, and the juices run clear when pierced. Removing the meat with tongs and shredding it gives you strands that absorb the peppery broth, creating luscious pockets of flavor. The sound of the meat tearing is subtle but satisfying, and the texture after shredding should be soft, not stringy. Returning the shredded chicken back to the crockpot allows it to finish soaking up the cooking liquid and spices. Avoid leaving large unshredded pieces, which can leave the chili inconsistent in texture. A common mistake is shredding on a hot plate where steam condenses and makes the meat soggy; shred over the pot or a stable surface and return to the crockpot promptly.
Serve warm!: The final bowl should feel invitingly hot, with steam rising and a smoky sweet aroma from the roasted pepper base. You should notice a gentle creaminess from the blended peppers, the tender chicken threads and the soft bite from the kidney beans. Taste and, if needed, adjust seasoning lightly with an extra pinch of salt to brighten the finish. A simple serving check is to spoon a bit onto a small plate, letting it cool for a moment, then tasting so you can sense the balance properly. A frequent misstep is serving too hot to taste, which can mask seasoning flaws; let a spoonful cool slightly before final adjustment.