One-dimensional (1D) carbon chains or carbynes consist of unique electronic properties that are highly suitable for electrical sensing of biomolecules such as DNA based on conductance change. In addition, the single atomic width of a carbyne enables the possibility of ultra-high spatial resolution in the measurement of individual DNA bases when compared to other carbon-based nanostructures such as graphene and carbon nanotubes. The present paper describes a quantum simulation of the interaction between a carbyne and different DNA bases using the density functional theory (DFT) and non-equilibrium Green's function (NEGF). Specifically, the transmission probability functions and density of states (DOS) of the carbyne are first computed and then used to determine the I-V characteristics of the carbon chain in the presence of DNA bases. The simulation results indicate that the carbyne's conductance increases when a DNA base is adsorbed onto its surface. This increase is the most significant with base A for a positive biasing voltage, and base T for a negative voltage. The result of the numerical study suggests that 1D carbon chains can be utilized as electrical sensing elements in DNA sequencing devices due to their capability in discriminating DNA bases.