Yes, this is the etymological root of ‘chlamydia’.

chla·mys /ˈkleɪmɪs, ˈklæmɪs/

-noun, plural chla·mys·es /ˈkleɪmɪsɪz, ˈklæmɪ-/, chlam·y·des /ˈklæmɪˌdiz/
a short, fine woolen mantle worn by men in ancient Greece.

[Origin: 1740-50; < L < Gk chlamýs]

Source: Dictionary.com.

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