Chechens
The main language of the Chechen people is Chechen. Chechen belongs to the family of Nakh languages (Northeast Caucasian languages). Literary Chechen is based on the central lowland dialect. Other related languages include Ingush, which has speakers in the neighbouring Ingushetia, and Batsbi, which is the language of the people in the adjoining part of Georgia. At various times in their history, Chechens used Georgian, Arabic and Latin alphabets; as of 2008, the official one is now the Cyrillic script of Russia.
Chechens
The Nakh languages are a subgroup of Northeast Caucasian, and as such are related to Nakho-Dagestanian family, including the languages of the Avars, Dargins, Lezghins, Laks, etc.
However, this relationship is not a close one: the Nakho-Dagestani family is of comparable or greater time-depth than Indo-European, meaning Chechens are only as linguistically related to Avars or Dargins as the French are to the Russians or Iranians.