Peel and finely chop the onion and carrot. Trim the dry ends from the celery and finely slice it.
Warm a deep frying pan over a medium-high heat for 2 mins. Add ½ tbsp olive oil and the chicken breasts. Fry for 4-5 mins till browned underneath, then flip and fry for another 4-5 mins till browned all over. Lift the chicken out of the pan and pop onto a plate.
Add the chopped veg to the pan with 2 tbsp water and a pinch of salt and pepper. Pop a lid on the pan (or use a baking tray to cover it if you don't have a lid). Turn the heat down to medium-low and cook for 8 mins, stirring now and then, till the veg have started to soften.
While the veg gently cook, peel the sweet potato and chop it into ½cm dice. Peel and finely chop the garlic. Drain the lentils and rinse them under cold water. Crumble the stock cube into a jug and stir in 400ml boiling water to dissolve it.
Stir the garlic into the veg. Cook and stir for 1 min till the pan smells sweet. Add the potatoes and lentils to the pan. Gently turn everything over a few times to mix it all in.
Nestle the chicken breasts back in the pan and pour in the stock. Cover. Turn the heat up and bring to the boil. Once it's started bubbling, turn the heat down to medium-low and simmer for 20 mins till the chicken is cooked through. While the chicken cooks, finely chop the tarragon leaves.
Taste the lentils and add a pinch more salt and pepper, if you think they need it. Spoon the lentils and chicken into warm, shallow bowls. Garnish with the chopped tarragon to serve.