In a 10-inch high-sided saute pan, bring 1 inch of water (about 4 cups) to a boil over high heat. Add the penne and the salt. Cook, stirring often, until the pasta is al dente, about 9 minutes; there should be a little water left in the pan.
Sprinkle the pecorino over the pasta; toss to coat. Add the tomatoes, chile paste, chives, lemon zest, lemon juice and olive oil, and toss.