The lipid bilayer is a flexible matrix that is able to adapt in response to the perturbation induced by inclusions, such as peptides and proteins. Here we use molecular dynamics simulations with a coarse-grained model to investigate the effect of a helical inclusion on a lipid bilayer in the liquid disordered phase. We show that the helical inclusion induces a collective tilt of acyl chains, with a small, yet unambiguous difference between a right- and a left-handed inclusion. This behavior is rationalized using the elastic continuum theory: The magnitude of the chiral (twist) deformation of the bilayer is determined by the interaction at the lipid/inclusion interface, and the decay length is controlled by the elastic properties of the bilayer. The lipid reorganization can thus be identified as a generic mechanism that, together with specific interactions, contributes to chiral recognition in phospholipid bilayers. An enhanced response is expected in highly ordered environments, such as rafts in biomembranes, with a potential impact on membrane-mediated interactions between inclusions.