Scrub the new potatoes and cook in boiling water with a large pinch of seasalt for about 10–15 minutes until cooked.
While the potatoes are cooking, put the crème fraiche and mayonnaise in a serving bowl. (You can use low fat versions of these if you prefer) and whisk together with a fork.
Drain the potatoes, turn off the heat. Put the potatoes back into the saucepan and add the butter/olive oil, lemon zest, a pinch of seasalt and a good few twists of freshly ground black pepper. Stir them about so that they become coated in the oil/melted butter.
Add the contents of the pot into your serving bowl with the chopped chives and mix well so that all the potatoes are coated in the dressing. It is important to do this while the potatoes are still hot.