I'm not certainly sure wich city is the cheapest, nevertheless, the cost of living in Chile is more or less like this (in US dollars):
Rent ($/month): from 200 to 800 (small house or apartment to a bigger house (140 m2))
water: $1,5/m3, including water treatment
electricty: $ 1,3 kWh
Telephone: $30 -40/month (fixed line).., mobile $30 up to infinite.. ($0.2/min)
Cable TV: $28/basic 56 channels
Internet: from $35 and up, depending of the speed.
Gasoline: $0.77/liter
Groceries: it depends of the size of a family. We are 5 at home, and I spend about $500/month (including everything, meat, vegetables, cleaning things, care stuff, etc..
Coca-cola: $0,65/liter
Milk: $0,82/liter
Bread: variable, regular bread $1.23/kg
Newspaper: $1.1
City bus (variable): around $0,5/ride
Metro (santiago): 0.65/ride
Tolls (highways): $2.8/100 km
Cinema: $6