Chakra is currently in pre-alpha, so installation is definitely not straightforward
You will need clang/llvm, dotnet, and make to install Chakra.
Clone the repository from Github:
$ git clone https://github.com/gamebox/chakra-lang
$ cd chakra-lang
Then use make to install
$ make
$ make install
This should build the compiler and the runtime object file and put them the former into a place likely to already be in your PATH.