Grill poblano peppers over open flame until well charred. Place in a plastic bag, seal, and let steam for 15 minutes. Remove charred skin, stems, and seeds. Dice.
Prepare cheese sauce using chicken stock instead of water. Reduce heat to a simmer.
Sauté onions in vegetable oil until just tender. Add chopped Anaheim peppers and sauté for 2 more minutes. Add to cheese sauce along with chicken and poblano peppers.
Simmer for 15 minutes, stirring frequently. Remove from heat and stir in lime juice.
Season tortilla strips with salt. Top each bowl with tortilla strips and serve.