Criminal background checks and police records are only required when applying through the Chilean consulates or embassies for visas to Chile. The department of immigration in Chile does not require criminal background checks, police records, FBI criminal reports when applying for visas in Chile.

The reason for the difference is that the department of immigration in Chile and the department of foreign ministry in Chile that operates the Chilean consulates and embassies are two different offices with distinct internal procedures. The recommend method for applying for a residency visa, including work visas and student visas, by the department of immigration in Chile, is to first enter the country under a tourist visa and then apply directly through their office where you will be living in Chile.  

Also some Chilean embassies may require a AIDS tests and other requirements. None of which are required if you apply in Chile for your residency visa at the department of immigration.

Even if you should choose to apply for residency through a foreign consulate of Chile, a criminal record may not disqualify you immediately from obtaining a visa. There are crimes and there are crimes, and some crimes considered serious in one country are not even considered crimes in others; at least not serious crimes. For example, what would be considered very serious felony marijuana possession charge in certain parts of the United States, would likely not be even prosecuted in Chile. What the Chilean government is more concerned about is people using Chile to flee prosecution, avoid jail, or people with long and violent criminal records. In most cases, if you have completed your sentence according to all requirements of the court, Chile will overlook prior convictions for most minor crimes. This is only in relation to applications for Chilean residency through the Chilean consulates and embassies.

Again, to be very clear, there is no criminal background check required when applying in Chile at the department of immigration.

If you are a wanted criminal or you are intent on committing crimes in Chile, we would caution that Chile is likly not the best place for you to take up residency. Regardless of how you are granted your visa, every foreigner in the country when they recieve a visa is required to register with the Chilean PDI (Chilean INTERPOL / FBI), submit finger prints to the national database, register their address, and the PDI does random checks to make sure foreigners have registered real addresses. So, for real criminals,  it would be better to move on to a more corrupt and disorganized country. Don't come to Chile. For everyone else, welcome to Chile.