Preheat the oven to 220°C (425°F) with a rack in the centre. Line a large rimmed baking sheet with parchment.
Cut the potatoes into 2.5 cm (1 inch) chunks and toss them on the tray with 1 tbsp of the oil and a pinch of the salt.
Roast the potatoes on their own for 15 minutes to give them a head start.
Meanwhile, cut the chicken into 3 cm (1 1/4 inch) cubes, the peppers into chunks and the red onion into wedges. Toss with the lemon juice, the rest of the oil, the oregano, minced garlic and the rest of the salt.
Add the chicken and vegetables to the tray in one layer and roast 20 minutes more, stirring once, until the potatoes are golden and the chicken reaches 74°C (165°F).
Grate the cucumber, squeeze it dry and mix with the Greek yogurt and chopped dill.
Serve straight from the tray with the cucumber yogurt.
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