The cell cortex is an active viscoelastic self-deforming sheet at the periphery of animal cells. It constricts animal cells during cell division. For some egg cells, the actomyosin cortex was shown to exhibit counter-rotating chiral flows along the axis of division. Such chiral surface flows were shown to contribute to spatial rearrangements and left-right symmetry breaking in developing organisms. In spite of this prospective biological importance, the effect of chiral forces on the flows and emergent shape dynamics of a deformable surface are completely unknown. To shed a first light on that matter, we present here a numerical study of an axisymmetric viscoelastic surface embedded in a viscous fluid. We impose a generic counter-rotating force field on this surface and study the resulting chiral flow field and shape dynamics for various surface mechanical parameters. Notably, we find that the building of a neck, as is observed during cell division, occurs if the surface contains a strong shear elastic component. Furthermore, we find that a large areal relaxation time results in flows towards the equator of the surface. These flows assist the transport of a surface concentration during the formation of a contractile ring. Accordingly, we show that chiral forces by themselves can drive pattern formation and stabilise contractile rings at the equator. These results provide first mechanistic evidence that chiral flows can play a significant role to orchestrate cell division.