Put the carrots, onions, lemon zest, dill sprigs, and olive oil in a 7-liter pressure cooker. Season the vegetables with the 1/2 teaspoon salt and the chicken with salt, to taste. Pour the broth in the pot, then nestle the chicken meat side down on top of the vegetables.

Close the pressure cooker lid, bring the pressure up to high (this can take up to 10 minutes). Adjust the heat, if necessary, to maintain an even high pressure for 10 minutes. Remove from the heat and use the quick-release method to bring down the pressure.

Stir the chopped dill into the chicken stew. Put 1 chicken breast in each of 4 large soup bowls and ladle some carrots and broth over each one.