We present a parallel device independent quantum key distribution (DIQKD) protocol based on the CHSH game and prove its security. Using techniques developed for analysing the parallel repetition of anchored non-local games, we show that the answers on a small random linear subset of the games in the DIQKD protocol can be simulated as the output of a single-round strategy for playing the CHSH game. Then, we use the recently developed unstructured approximate entropy accumulation theorem to establish the smooth min-entropy lower bound required for the security proof. Our approach yields a more information-theoretic and general proof for parallel DIQKD compared to previous proofs.