It refers to something annoying, rat-looking, in a way ugly, loud and tiny. Used separately in response.
Stephanie: OMG the way he ran was soo funny!
Nicole: I know right! His face! Like a chihuahua!
Stephanie: hahaha
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to be utterly excited about something to the point of near uselessness.
Did you see how excited Bill was when he met Mary? He was shivering like a chihuahua!
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Person 1: Hey dude, you're shaking a lot.
Person 2: Yeah, I'm shakin' like a scared chihuahua