As early as 4 months and to as late as 2-3 years
If by periods you mean heat cycle then it is fact that chihuahuas are small dogs and can get their first heat cycle early. Usually dogs get their first heat cycle at the age of 6-8 months. Small breeds can get early while large breeds late first heat cycle. Heat cycle in dogs can be of 3-4 weeks with average of 3 weeks. Heat cycle in dogs starts with swelling of vulva and bleeding which can last for 7-10 days.
Usually they go in heat the first time about 6 months
My lil chihuahua just came in heat today, she is about 3 days from being 6 months old.
My friends chihuahua got her period when she was 2months old. But it varies between dogs and they types. Usually within 6 months.
We have a female and she was almost 1 year old. She is 2 yrs old now and has only been "in season" a total of 2 times.