|You are incorrect that you cannot break him of this. Chihuahuas are highly trainable, you just need to know how to approach it.
He's likely not had a good life prior to becoming yours, he may never have been taught how to behave. He may also be very nervous and frightened. Chihuahuas bond to only one or two people who become the center of their universe. He may be afraid he'll lose you, so he has to protect you. A way to increase his confidence is basic obedience commands, never feed him while you're eating, be pack leader in all ways. You go through doors first, you eat first and finish before he gets anything (and I really discourage the feeding of people food). He can have a small biscuit if he has been good and waited patiently and quietly while you ate. He'll be much less excitable as he learns his place in the pack, and as he approaches adulthood (about 1 1/2 years).
Start with one person at a time, have that person come to the house for a few minutes. When people come to the house, he will likely bark, that's his job, to alert you to the presence of a stranger. Pick him up and have him in your arms, this way he feels safe, and tell him "good dog, quiet now". Welcome the person/people in, introduce the dog to them and allow him to sniff their hands. The guests should not try to pet him, just let him get their scent. You are pack leader, you have welcomed them into the den. He has done his job of alerting you, now his job is done and he should be quiet. If he continues to bark, he should be ignored. Chi's hate to be ignored, as soon as he figures out that barking means no attention, he will stop. As soon as he is quiet, even just for a second, praise him for being quiet and give him attention, stop if he starts barking again. If the dog approaches the guests, ask them to remain quiet, extend their hands and make no motion to pet him. If he tries to touch or lick their hands, they can slowly pet his chest, palm up. Coming at his head palm down from above is scary, so don't do it. I don't even after having mine for years, I pet the chest first and then the head.
With repeated experience, he should settle down more. Of course, if he snarls or snaps, that has to be dealt with right away. Don't hit, but give him a stern "NO" and remove him from the room. Give him a time out and if he is quiet in another part of the house, re-introduce him a few minutes later, praising him for not snarling.