Could it be hiccups? That's the only rhythmic sound I can think of that's not the result of a respiratory infection. But my rats that hiccuped never seemed uncomfortable when doing it. I found that with one rat in particular, simply picking him up would stop the hiccups. And people here on GM have posted about rats' hiccuping from happiness.
Come to think of it, I did have a rat once who made a noise while breathing that could quality as a chirp. Antibiotics didn't help, and the vet eventually concluded that it was caused by a benign structural abnormality of the nasal passages.
Is this something that other Holbrook rats do, perhaps? (My beautiful sweet Lizzie's seizures turned out to be common to the runts of the South Paris litters.) At least if the problem were common to other, related rats, it'd probably not be the result of some dire disease.