During our trip to Southern Peru, Bolivia and Northern Chile in September of 2015 we did a 5 day/4 night trek with Bolivian Journeys in the Condoriri Mountains outside of La Paz, Bolivia. While I would not recommend Bolivian Journeys, the scenery was amazing. For experienced hikers it is possible to hike in these mountains on your own, but for safety reasons I would suggest finding a reputable trekking company.
Review of Trekking Company
Bolivian Journeys – First World Prices, Third World Service
This review of the trekking company we used also includes an overview of the hike.