Peel carrots, cut into 2-inch (5 cm) lengths, and boil in salted water for about 10 minutes, until tender but still firm. Put thicker pieces in first so they finish together.
Drain and cut lengthwise into sticks about 1/4 inch (0.5 cm) thick. Put in a small, deep serving dish.
Smash the garlic clove to loosen the peel, peel it, and bury it among the carrots. Add oregano, salt, pepper, vinegar, and enough olive oil to cover.
If serving the same day, let marinate at room temperature at least 3 hours. If making ahead, cover and refrigerate, then bring to room temperature 2 hours before serving. If keeping longer than a day, remove the garlic after 24 hours.