In this paper, we propose a new polar coding scheme with molecular programming, which is capable of highly parallel implementation at a nano-scale without a need of electrical power sources. We designed chemical reaction networks (CRN) to employ either successive cancellation (SC) or maximum-likelihood (ML) decoding schemes for short polar codes. From ordinary differential equation (ODE) analysis of the proposed CRNs, we demonstrate that SC and ML decoding achieve accurate computations across fully-parallel chemical reactions. We also make a comparison in terms of the number of required chemical reactions and species, where the superiority of ML decoder over SC decoder is observed for very short block lengths.