|Welcome to the world of chihuahua ownership. She whines because she has bonded with you, she wants to be with you all the time, and you leave her. I don't know the circumstances of how and why you acquired her, but she is likely afraid she will be abandoned again.
Chihuahuas bond very closely with one or two people, and even if they have gone through several changes of owner, they still remember their previous owners with great affection. She is likely grieving for her previous owners, other dogs she knew, etc. The bad side is that they have to be taught to tolerate separation, and I do mean tolerate, they will never be happy to be separated from "their humans".
I suggest you start by one of you leaving and the other staying with the dog. Just go outside, shut the door, wait 10 seconds and come back in. Praise her for being quiet, and reassure her that Mommy and Daddy will ALWAYS Come Back. Then repeat with the other person. Gradually start extending the time you are gone, and start having both of you leave, she will become more comfortable as she trusts that Mommy and Daddy will ALWAYS Come Back.
If she whines, you have to shorten the time so that there is a period, no matter how short, before she cries. That is when you praise her. Make sure she has toys and perhaps a t-shirt or something that has your scent on it, this will comfort her.
You may want to confine her to a room where there isn't anything she can chew on except approved toys. This is for her benefit, not yours. This may also help her adapt to being left alone, use a baby gate rather than shutting the door so she can still see you. As always, brief periods extending, for the most part when you are home she should be with you. Never do this as punishment!!!
Also, don't make a big deal about going, if you start making a fuss and telling her how sorry you are and etc. etc. it will only make it worse. When it's time for me to leave for work, I sit down on the loveseat. I ask for kisses. Then I get up, tell my two girls that "Mommy has to go to work now, be good girls while Mommy is gone, then Mommy come home play with Nixie and Gremlin", collect my bags and go to the door. They follow, I open the door and tell them "Bye Bye, be good while Mommy is gone", close the door and get in my car. That's it. That worked when I had only one chi, and just as well now that I have two. They hop up on the back of the loveseat to look out the window, but they're quiet and once the car has pulled out of the driveway, they curl up on the loveseat under their blanket or in the sunshine and that's that until I come home.
That didn't happen overnight, it took some time to teach them that I would always return, but it did happen. She likely bounces all over you when you come home, let her be happy, but if you don't want jumping do the same thing as when you leave, just come in, ignore her for a minute or so, then pick her up, play with her, etc. When leaving and returning aren't any big deal to you, it becomes less of a big deal to her.
I recommend the book Chihuahuas for Dummies, by far the best book on the care of these adorable creatures.