Cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 2 cups pasta cooking liquid.

Meanwhile, pulse almonds in a food processor until smooth. Add parsley, chives, oil, and Parmesan; process until smooth. Season pesto with salt and pepper.

Toss pasta and pesto in a large bowl, adding pasta cooking liquid by 1/4-cupfuls until saucy. Season with salt and pepper.

DO AHEAD: Pesto can be made 5 days ahead. Cover surface directly; chill.