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A chirping or singing guinea pig is a rare thing, I've had guinea pigs for 24 years of my life and I have only heard it a few times. It sounds like there is a bird in their cage. Really!
It happens rarely enough that there is no general consensus on what it means.
Some theories are:
Loneliness / wanting attention / being bored.
Not liking something that is happening. (My one guinea pig would usually chirp when I would doze off in the living room and start snoring. He didn't like my snoring.)
Mourning. I have heard of guinea pigs chirping when their bonded companion dies.
The first time I heard it, I was startled, and my mother and I were convinced there was a robin in the house. Instead it was our little Caesar making the noise. I suspect he did it because he heard my mother and me talking in another room, and he adored my mom and he probably didn't want to be left out of the fun of being with his human. :) While it is only speculation, he seemed overjoyed when he got cuddles from her.
One of the best things to do for loneliness besides getting a companion is I spread a blanket on the floor and then put a guinea pig playpen on it. (Just make sure none of your other pets can get to the guinea pigs!) Then I fill it with a few cardboard boxes, paper bags, and my guinea pig adores running through his crinkle tunnel.