The absence of a straightforward strategy to interface native D-DNA with its enantiomer L-DNA oligonucleotides of opposite chirality are incapable of forming contiguous Watson-Crick base pairs with each other-has enforced a "homochiral" paradigm over the field of dynamic DNA nanotechnology. As a result, chirality, a key intrinsic property of nucleic acids, is often overlooked as a design element for engineering of DNA based devices, potentially limiting the types of behaviors that can be achieved using these systems. Here we introduce a toehold-mediated strand-displacement methodology for transferring information between orthogonal DNA enantiomers via an achiral intermediary, opening the door for "heterochiral" DNA nanotechnology having fully interfaced D-DNA and L-DNA components. Using this approach, we demonstrate several heterochiral DNA circuits having novel capabilities, including autonomous chiral inversion of DNA sequence information and chirality-based computing. In addition, we show that heterochiral circuits can directly interface endogenous RNAs (e.g., microRNAs) with bioorthogonal L-DNA, suggesting applications in bioengineering and nano medicine. Overall, this work establishes chirality as a design parameter for engineering of dynamic DNA nanotechnology, thereby expanding the types of architectures and behaviors that can be realized using DNA.