In the 1978 Chilean law Control de armas (Nº 17.798), the rules for civilian gun ownership is explicitly laid out.
The Ministry of National Defence was the overall overseer and in control of civilian gun ownership in Chile at this time. In this particular law, the Ministry of National Defence was to watch over and control the following: any type of weapon, including small arms, artillery pieces ("el material de uso bélico") etc., all sorts of ammunition and explosives, chemical substances used in the making of weapons, as well as fireworks and other pyrotechnical devices. (Article 1 and 2).
According to article 3, no one (read: civilians) were supposed to be in ownership of any sort of automatic weapon, including machine guns, submachine guns and automatic rifles. It also adds that you are not allowed to own any sort of automatic weapon or semi-automatic of great "destructive or effective power, either by its power, by the calibre of its projectiles or by its aiming ability [presumably referring to powerful scopes]".
With that said, you can read article 3 as to say that you could own a handgun or a hunting rifle. Article 5, for example, lays out the rules for a civilian who owns a gun "not mentioned in article 3". It states that the owner is supposed to report to the proper authorities at which time all personal details are written down.
Article 5a makes the following requirements on a gun owner: You have to be of legal age, have to have a known residence, have to prove to be in the possession of the proper knowledge of the maintenance and use of the firearm as well as the right physical and psychological capability, have no known criminal record or a history of violent behaviour (such as domestic violence).
Every five years, you had to prove that you could still fulfill these requirements.
Article 5 also points out that the registered firearm is only authorized to be kept in the home of the owner, at the place of work or at the location that the owner "hopes to protect". If you wanted to move the firearm from one location to another, you needed proper authorization for it. The only individuals who were allowed to carry weapons more freely were hunters or athletes who could apply for a permit that lasted for 2 years.