Bring vinegar and next 4 ingredients to a boil in a medium saucepan. Stir to dissolve sugar. Remove from heat.
Cut cucumber into 1⁄8-inch-thick slices (about 31⁄2 cups slices). Thinly slice onion into quarter rounds (1 cup slices). Thinly slice peppers, leaving seeds intact.
Divide vegetables between 2 (16-ounce) jars. Carefully pour vinegar mixture over vegetables to fill jars. Screw the lids on jars and chill 1 day before serving. Store pickles in refrigerator up to 1 week.