If you have European citizenship, you are issued a tourist visa, the so called „Tarjeta de Turismo“when you enter the country. This Visa is granted for 90 days and you can extend it in Chile for 100.00 USD once for another 3 months.
Please note that your passport needs to be valid for at least another 6 months and that you have to return the „Tarjeta de Turismo“when leaving the country. Should you lose it you need to apply for another one in Chile before your departure.
You can find further information on the website of the Department of Foreign Affairs.