Finely chop the fresh tarragon (or measure out 2 teaspoons if using dried). Sprinkle over the chicken breasts, then season with salt and pepper. Pour the olive oil over the meat, cover, and refrigerate for 2 hours, turning once halfway through.
Prepare the peaches: If using fresh peaches, scald each for 30-60 seconds until the skin slips off easily, then peel, halve, and remove the stone. If using canned peaches, simply drain them. Blend 3 of the peaches (or 6 halves if using canned) with an immersion blender until smooth. Dice the remaining peach (or 2 halves if using canned) into small pieces and drizzle with the lemon juice.
Heat the marinade oil in a large frying pan over medium-high heat. Fry the chicken breasts until golden brown on each side, about 4 minutes per side, until they reach an internal temperature of 74°C (165°F). Remove the chicken and set aside to keep warm.
Finely dice the onion. Fry it in the same pan for 1-2 minutes until softened. Pour in the cream, scraping up any browned bits from the bottom of the pan. Stir in the peach puree, coffee powder, and vegetable stock. Season with salt, white pepper, and a pinch of curry powder, adjusting to taste and adding more tarragon if desired.
Return the chicken and diced peach pieces to the pan with the sauce. Simmer gently for 8-10 minutes until heated through. Serve immediately.