Moiré superstructures arising at twisted 2D interfaces have recently attracted the attention of the scientific community due to exotic quantum states and unique mechanical and tribological behaviors that they exhibit. Here, we predict the emergence of chiral distortions in twisted layered interfaces of finite dimensions. This new phenomenon originates in intricate interplay between interfacial interactions and contact boundary constraints. A metric termed the fractional chiral area, is introduced to quantify the overall chirality of the moiré superstructure and to characterize its spatial distribution. Despite the equilibrium nature of the discovered energetic and structural chirality effects they are shown to be manifested in the twisting dynamics of layered interfaces, which demonstrates a unique continuous transition from stick-slip to smooth rotation with no external trigger.