Add the feta, Greek yogurt, lemon juice, and olive oil to a small food processor. Blend until smooth, scraping down the sides once or twice.

Fold in the chives and black pepper. Taste with a piece of radish before adjusting. Add cold water a teaspoon at a time only if the mixture is too thick to scoop.

Spoon into a shallow bowl, scatter a little more chive over the top, and serve with washed, thoroughly dried radishes. Halve large radishes for easier dipping.