You probably really love your dog and you may actually be happy when he jumps up to greet you when you come home, but this is not always practical for you or for other people that may come over to your house to visit. Many people are a little scared when dogs jump up on them. Your friends and other visitors may wear very nice clothing that they don't want ruined by accident. Sometimes you may have a few large grocery bags in your arms that you are carrying in from the store or you may have some expensive clothing on that you happened to wear for work or a special occasion. It is up to you whether you want to routinely allow your Chihuahua to jump up when he greets you. If you decide that you don't want your dog to jump up, you will need to teach him not to do this and be consistent about it.
To teach your Chihuahua not to jump up, you can gently help him get back down when he jumps up on you and tell him to sit and give him nice praise when he obeys you. Then, you can stoop down to your dog's level, while he is sitting and let him give you his happy greeting the way he wants to, while he remains in the sitting position. It is good to be consistent when teaching your Chihuahua not to jump up when greeting you, so he doesn't get confused.
For example, if you are wearing your old bluejeans on the weekend or your gym clothes after a work out and you think it is OK for him to jump up during these times, but not when you are wearing your expensive clothes, he will get confused. The important thing for your Chihuahua to understand is that he still is allowed to greet you in his own special way, but instead of jumping up, it will be in a sitting position. If you continue to praise your Chihuahua when he obeys, he will probably quickly learn what is expected of him and be happy!