Cut the ends off the plantains and peel. Cut in 11/2-inch chunks.
In a shallow bowl, pour 1 cup water, the garlic, and the salt, and mix a little with a fork. Set aside.
Pour the oil into a deep, medium, heavy pot, and place over medium-high heat. When the oil is hot (about 350 F), add the plantain pieces a few at a time, and fry 6 to 8 minutes. (If the oil doesn’t cover the pieces, fry for 4 minutes, turn and leave 4 more minutes). Remove the plantains from the oil with a slotted spoon.
On the work surface, place a piece of plastic wrap, put the pieces of plantain on it, and cover with another piece of plastic. With a heavy pot, press well on the pieces of plantain, until they become very thin (1/4 inch) and even.
Dip each thin slice in the garlic water for a couple of seconds, and fry again in the same oil at 350F for 2 to 3 minutes on each side. Remove them with a slotted spoon and drain on paper towels.
Add more salt if desired and serve with lime wedges.