Chihuahuas aren't the worst breed when it comes to escaping every means of containment possible. They simply can't scale fences, jump as high, or bite and pull as hard as many of the larger breeds. Chis are, however, very athletic, and they often exceed their owner's estimations.
If your puppy is a virtual jumping bean, she will be able to escape puppy playpens, baby gates, and low fences. If you find this is the case, you may need to get a little creative. Use a puppy playpen that has a top or wire roof. For those pups escaping a lower baby gate, consider double-gating a doorway (putting one pressure gate above the other) or using a dog gate that is taller and meant for jumping, scaling puppies. If your outdoor fence is too low to contain your Chi, you'll need to add to your present fence. (Some fences allow the addition of a foot of lattice to the top.) You might also consider replacing the fence with a taller one or always supervising your Chi when she is in the backyard.
Have Head, Will Follow
Chihuahua puppies can be very, very little. The spaces through which they can scramble through to escape their containment or barrier often appear impossibly small. The basic rule of thumb is that if a puppy can wriggle her head through a space, she can wriggle her entire body through. Spacing in your outdoor fence (between slats or the chain links), a window that's cracked open, a crate door that can be pushed open when it is latched on top but not on the bottom, a small tear in a porch screen, or a gap between a door and the floor could all be escape hatches for a little puppy.
Be cognizant of just how small your puppy is, and look for ways in which she could escape, should he set his mind to it. The answer to escape problems is exercise, exercise, exercise! If your Chihuahua is pooped out, chances are she won't be looking for something do — she'll just want to snooze. If your well-exercised puppy possesses a brilliant yet devious mind and is bent on breaking out of all barriers, keep her safely crated when you cannot supervise her every move.