Yes, the Niva is still being built as a co-product of AutoVaz and GM.
AFAIK, Chevrolet has bought both a trademark and a production line for a 1998 Lada Niva in 2002 and builds it to sell as a Chevy-Niva in Eastern Europe and Central Asia ever since.
About that time in 2002 Lada restarted a 1977 Niva, initially cancelled in Russia and outsourced for production and distribution in Peru, Egypt and Kazakhstan in 1998. As far as a name is now belongs to Chevrolet they are marketing an old one as Lada 4x4.