All major cities have both public and private hospitals, and Santiago, Concepcion and Valparaiso have several. The private 'clinicas' are more expensive, but there is usually little or no wait, and they can attend to most health problems. It is common practice for them to ask for a cheque or credit card guarantee first, so go prepared.
Chileans are not shy of medication, so you can find well-stocked pharmacies everywhere. Some drugs that require prescriptions in other countries, can be bought over the counter here. If you plan to stay for a lengthy period of time, it may be worth getting a discount card at one of the major pharmacy chains.
Water from the tap in Chile is very good, and should not cause problems for visitors. In rural areas with no water treatment, prefer bottled water.
Chile enjoys relative immunity to important diseases. Easter Island (Rapa Nui) is the only place where cases of Dengue fever have been reported. However, no further cases have surfaced and normal precuations against mosquito bites are considered to be sufficient. No cases of Cholera have been reported in over 10 years. Cases of HIV/AIDS are low, but do exist, so practice safe sex.