Whenever your dog acts shy, both people must ignore him. 100% completely and utterly ignore him. This will actually set off a chain of events that will help the Chihuahua come out of his shell.
There will be times that the Chi prefers to remain alone, often watching from a distance. Though, when humans ignore the dog - not trying to coax him out or pay any attention to him - something happens now and again... Curiosity will take over. When the atmosphere is calm, without any pressure to show himself or perform - a shy dog often on his own will venture out to see what is happening.
You see, when a timid dogs knows that there are no eyes on him, he will then feel safer to inspect things, to come a bit closer to hear conversations, to peer over to hands to see if they hold any treats. If he can smell a particular food, this will insure that he will be inquisitive about exactly where it is and how to go about getting it.
The key to this, is to make sure that the dog does indeed receive confirmation that there is a treat for him. Plan this with your guest in advance. As soon as he or she enters the premises, indiscreetly give that friend a treat for just this moment. Have one in your hand as well.
A crispy piece of bacon works amazingly well for this type of training. Pre-cooked microwave bacon - with grease blotted out via paper towels - is only 40 calories
a slice. With both people holding a 1/2 slice, this is 20 calories for each treat.
As the Chi - insecure as he is - slowly comes over to sniff or see just what you are both holding, without saying his name or making a big deal out of things, each of you can extend your hand and allow the Chihuahua to retrieve the snack from whomever he wishes.