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A chibi-fied version of Tsuruya from Suzumiya Haruhi no Yuuutsu, created by Eretto in post #47838.
The two have fairly dissimilar personalities. Whereas Tsuruya is easily excitable and laughs a lot, Churuya seems more simple-minded, and has a deep appreciation for smoked cheese. Her signature catchphrase is nyoro~n.
Churuya first appeared on Eretto's website in a now famous 4koma (post #47838). Churuya inherited Eretto's love of smoked cheese. Notably, in the last panel Churuya utters her catchphrase nyoro~n when she becomes disappointed by the lack of smoked cheese. Likely one major reason for Churuya's popularity is the sense of schadenfreude at Churuya's perpetual misfortune.
From the very start, fan reaction to Eretto's Churuya comics was wildly positive. After being linked on 2channel, Eretto's site would frequently go down because of all the traffic. Eretto continued to write new Churuya-san 4koma, and has even anthologized them in doujinshi.
Churuya became a meme frequently used by other artists. Usually the one common factor is the last panel, where a character drawn in the style of Churuya (complete with :3) says nyoro~n or some variation thereof.