I translated text strings into Chuvash on translatewiki.net which is used for the translation of wikimedia projects and external projects. Thanks for the tip to @aharoni and Sakha Wikipedia mailing list. If you can write Chuvash, please feel free to correct and add new text strings.
How to use
To be able to see the Chuvash interface we have to have a Chuvash locale. Unfortunately there is no one. If you are using Android then you are a lucky one, you can add any locale with MoreLocale 2 app. Just install it and add a new locale (cv or cv-RU): By the way, to write with additional four letters in Chuvash (besides the Russian 33 letters), you can use the Chuvash keyboard layout for Android which I published on Google Play. The most interface on your mobile will use default strings (English), but Wikipedia Mobile’s interface will be completely in Chuvash :)