Why not use th articla "an" in the sentence "Chen ki mouri a" if the article modifies "chen"?

The article you use depends on the words that come before the article. In that case it's "mouri".
FYI: the article 'an' may follow the word "mouri" also because of the nasal  "ou" sound in "mouri"
so you can also say "Chen ki te mouri an".

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