For suggestions on hiking and climbing in the vicinity, see Parque Nacional Los Glaciares [1].
From El Chaltén [2], it’s possible to arrange a one-day trek and ice climb on Glaciar Torre (US$45 pp) with Fitz Roy Expediciones (Lionel Terray 212, tel./fax 02962/493017, www.fitzroyexpediciones.com.ar [3]), which also offers lengthier guided hikes—nine-day expeditions, really—on the Campo de Hielo Sur, the Southern Continental Ice Field (US$950 pp). Oscar Pandolfi Expediciones (San Martín s/n, tel. 02962/493043, www.caminoabierto.com [4]), Alta Montaña (Lionel Terray s/n, tel. 02962/493018, altamont [at] infovia [dot] com [dot] ar), and Viviendo Montañas (Av. Güemes 68, tel. 02962/493068, www.vivmont.com.ar [5]) also conduct ice field expeditions.
NYCA Adventure (Cabo García s/n, tel. 02962/493093) offers half-day excursions including activities such as climbing, hiking, mountain biking, rafting, and rappelling. Lago San Martín (Riquelme and Rojo, tel. 02962/493045) arranges excursions to and from Lago San Martín, across the mountains to the northeast, with estancia accommodations.
Just north of Albergue Rancho Grande, Viento Oeste (San Martín s/n tel. 02962/493021, vientooeste [at] infovia [dot] com [dot] ar) rents and sells climbing, camping, and wet-weather gear. Eolia (San Martín s/n, tel. 02962/493066, www.patagoniamagica.com [6]) also rents gear and provides guide service.
Links:
[1] http://www.moon.com/destinations/chile/southern-patagonia/parque-nacional-los-glaciares
[2] http://www.moon.com/destinations/chile/southern-patagonia/el-chalten
[3] http://www.fitzroyexpediciones.com.ar
[4] http://www.caminoabierto.com
[5] http://www.vivmont.com.ar
[6] http://www.patagoniamagica.com