Braised Chard with Olive Oil and Rice

1 pound chard, washed and trimmed (you can also use kale, bok choy, or leeks)
1/3 cup extra virgin olive oil
2 small carrots, roughly chopped
Salt and freshly ground black pepper
¼ cup white rice
Juice of ½ lemon

1. Cut the stems out of the chard leaves.  Cut the leaves into wide ribbons and slice the stems; keep the leaves and stems separate
2. Put all but a tablespoon of the oil in a large skillet over medium heat.  When hot, add the chard stems and carrots, along with a sprinkling of salt and pepper and cook, stirring occasionally, until the chard is tender, about 15 minutes.
3. Add the chard leaves, som salt and pepper, the rice and 1½ cups water.  Cover, adjust the heat so the mixture simmers, and cook for about 30 minutes, or until the water is absorbed; the mixture should be moist but not soupy.  Serve hot, at room temperature, or cold.  Just before serving, drizzle with the remaining olive oil and the lemon juice.