In a large pot, combine potatoes with enough salted water to cover by 2 inches: bring to a boil over high heat. Reduce heat to a brisk simmer and cook until potates are completely tender in the center, 8 to 12 minutes, adding the green beans during the last 1 to 2 minutes of cooking. Drain, then return the mixture to the hot pot and let rest until very dry, about 2 minutes.

Meanwhile, in a food processor, pulse pine nuts and garlic until finely chopped. Add the parsley and pulse, scraping down the sides and bottom of the bowl, until well combined. With the machine running, drizzle in oil and purée until smooth. Transfer the pesto to a large bowl. Season with salt and pepper and add the chives and lemon juice: mix well.

Add warm potato mixture to the pesto and season with salt and pepper. Mix well. The salad can be made 3 hours ahead and kept refrigerated. Bring to room temperature and toss well before serving.