Several morphologies are observed in out-of-equilibrium systems. They can be highly symmetric as stripes, hexagons, or squares, and more complicated such as labyrinthine patterns. These shapes arise in different contexts, ranging from chemistry, biology, and physics. Here we study the emergence of chiral labyrinthine patterns near the winding/unwinding transition of a chiral liquid crystal under geometrical frustration. The patterns emerge due to morphological instabilities of cholesteric fingers of type 1. Experimentally, we show that when heating the cholesteric liquid crystal cell at different rates, the winding/unwinding transition is remarkably different. At low rates, chiral fingers appear and exhibit a serpentine instability along their longitudinal direction. At higher rates, after the chiral fingers nucleate, the splitting of their rounded tips and side-branching along their body is observed. Both mechanisms create labyrinthine patterns. Theoretically, based on an amplitude equation inferred by symmetry arguments, we study the morphological instabilities and characterize them by their interface curvature distribution. We discuss the possible velocity-curvature relationship of the finger rounded tips.