Cut outside from radishes in 1/4-inch-thick slices and discard white insides. Cut radish and onion into 1/4-inch dice. Wearing rubber gloves, seed jalapenos if desired and finely chop. Chop cilantro.
Halve and pit avocados. Scoop flesh into a bowl and coarsely mash with back of a fork. Stir in radish, onion, chiles, cilantro, lime juice, and salt. Serve guacamole with tortilla chips.