Cerro Gorra Blanca
Gorra Blanca is a 2,900m peak on the eastern edge of the South Patagonian Ice Cap, marking the border between Chile and Argentina. Whilst this isn't technically demanding it is a challenging expedition of 5 to 7 days, approaching over glaciers and the Ice Cap itself, with a thousand metre ascent on summit day.
The mountain, which was first climbed in 1964, presents great views over the Ice Cap (to the West) and out to Argentina (to the East).
Typically, you'd base yourself in El Chalten in Argentina, approach via the Rio Electrico and Piedra del Fraile and use La Playita as your basecamp. From there you head up the Marconi Glacier and over the Marconi Pass.
Luke attempted to climb Gorra Blanca in January 2011, but unfortunately the weather conditions only allowed his group to reach the Marconi Pass.
Map of Cerro Gorra Blanca