Heat olive oil in a large heavy-bottomed pot over medium-high heat.
Toss chicken thighs in cornstarch, just to coat, shaking off excess. Add chicken thighs to pot (in 2 batches) and sear on both sides until brown, about 3 minutes per side. Remove and set aside.
Reduce heat to medium-low and add onion and celery, sautéing until translucent, about 5 minutes. Add peppers and garlic and sauté 2 minutes more.
Flood pepper mixture with stock or water, add thyme and bay leaves and bring up to a simmer.
Return chicken thighs to liquid, cover and simmer gently for 45 minutes to 1 hour, until chicken is cooked through and peppers are tender.
Remove chicken thighs and bay leaves and purée sauce until smooth (an immersion blender works best) and strain. Return sauce and chicken to the pot and bring to just below a simmer. Season and stir in butter to enrich the sauce, if desired.