Chihuahua keeps barking at new puppy. How to stop?

It's only the first day, give her time to adjust.

There are no guarantees that any two dogs will get along, and you can't force them to anymore than anyone can force you to get along with someone you may dislike.

Not saying it can't be done, with constant supervision, separate/contain when you can't, immediate correction when caught in the act and if it doesn't work out re-home the pup.

Today !!!!!
Give the Chi more time to get used to having the pup around.
I expect she will soon be telling him off with growls and snaps and this should be allowed as long as she does not physically attack him.
Meanwhile always supervise the two dogs when together until you are certain they have bonded, which they will do, eventually. It may take up to 6 weeks though for the Chi to fully accept him.

rehome the new pup .....

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Chihuahuas can be very ferocious dogs. I personally don't like them because they yelp to defend themselves against bigger dogs because they know they are so small. They cause a lot of conflict when with other dogs that are bigger because they will just not shut up, and the other dog gets aggressive because the chihuahua is putting out an agrressive vibe and it will or may end up hurt. Aggressive behaviour like this in any dog needs to be stopped asap because you wouldn't allow it in a big dog so why a designer dog? It can transfer its behaviour to other humans and this is not ok. Chihuahuas are difficult to train so you would need to invest in a short time at a dog behaviour school and put it in its place like a normal dog not coddled like a baby.

why did u bring new dog. u knew his temperment.