In a medium lidded saucepan, combine the rice with 1 1/2 cups water. Bring to boil, turn the heat down to low, and cover. Cook for 20 minutes, until the liquid is absorbed and the rice is al dente. Remove from the heat and let stand for 10 minutes. Fluff with a fork.
Meanwhile, in a large mixing bowl, toss the carrots and radishes together with the vinegar and salt. Let sit in the mixture, stirring occasionally, until the rice is cooked, about 15 minutes.
Add the rice to the vegetables along with the chives and olive oil. Toss to combine. Transfer to a serving dish and garnish with additional chives.