Many people adopt a practice of avoiding travel with a passport having less than 6 months validity, because some countries require foreign passports to be valid for at least six months on entry, or even six months beyond the planned end of the visit. In some countries there is no 6-month rule, but rather than worrying about each country you plan to go to (and the possibility of having to go to countries you hadn't planned to), it may be simpler just to renew your passport early.
Having said that, Chile appears to have no six-month rule. Timatic, the database of entry requirements that airlines use to decide whether to allow passengers to board international flights, says "Passports and other documents accepted for entry must be valid on arrival." (You don't mention your nationality, but this came from a query submitted on the assumption that you are a citizen of the UK.) The US embassy in Chile has the more reasonable sounding "U.S. passports must be in good condition and valid for the period of stay" (source). It is however possible that Chile has different passport validity rules for different countries (as does the US, for example). I tried searching for information about that on Chilean government sites, but could not find any.