This can be either a hot side dish or a room-temperature salad.
WARM THE OLIVE OIL in a pan with the garlic and chile peppers.
Once the garlic slices are brown, remove them and set the oil and peppers aside.
Separate the chard stems from the leaves.
Cut the leaves into large pieces and wash them.
Trim the uneven ends off the stems.
Then, to make the stems as tender as possible, peel off the thin, transparent outer skin from each stem.
Catch the edge of a knife under the top layer of skin, and pull it down the length of the stem.
It sometimes helps, especially if the stem is cured, to first cut the stem in half lengthwise.
Peel both sides of the stems, cut them into 2-inch lengths.
Then lengthwise into narrow strips.
Peel the carrots, slice them into long, 1/4-inch diagonals, then into narrow strips.
Bring 4-to-5 quarts of water to a boil, and add 4 teaspoons of salt.
Briefly cook the chard stems and the carrots separately until each is tender--about a minute for the carrots, 2-to-3 minutes for the chard.
Remove them from the water and set them aside.
Plunge the chard leaves into the water and cook until they are tender, 3-to-5 minutes, depending on the quality of the chard.
When they are done, remove them to a colander.
Press against the leaves with the back of a wooden spoon to get rid of the water then put them in a bowl with the stems and the carrots, and toss them with the olive oil.
Season with salt and serve with vinegar or slices of lemon.