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Let us clear things up, there are two types of Chihuahua, long and short/smooth coat, there is simply no separate classification for the mythical 'Teacup Chihuahua' and it is not a separate breed... it is the micro pig of the dog world, and look how that turned out!
Any Chihuahua will fit in a teacup when it is a puppy, they are the smallest dog in the world after all, and as with most breeds of dog you will get a smaller than normal puppy in a litter, this is usually referred to as the runt.
Some puppies are born smaller for a number of reasons, including, but not limited to: disability, growth hormone deficiency, reduced nutrients in the womb, gestation position and genetics.
If they survive the first few days they can pull through but may end up with long term health problems, in very rare cases small puppies thrive once they get milk from their mother and grow into normal, healthy dogs but more often than not they do not survive without intervention.
We have been hobby breeding for many years, and have pretty much seen it all, the fads, the crazes the silly names, and just recently spotted an advert for a 'Micro Teacup Chihuahua' no less.
Glamour Chihuahuas or any reputable breeder would never advertise a 'Teacup Chihuahua', they can't be registered as such, they can't be shown as such.
Don't get mugged off (pun intended), your Chihuahua will no longer fit in a teacup when it is a few months old, so if you are being advertised a 'Teacup Chihuahua' simply walk away... you wouldn't pay more for a broken down car, or dilapidated house now would you!