In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [λ] and Josephson [λJ] lengths, α = λ/λJ. The chain is composed of tilted vortices at large α’s (tilted chain) and at small α’s it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate α’s and found two types of phase transitions. For α ≲ 0.6 the ground state is given by the crossing chain in a wide range of pancake separations a ≳ [2–3]λJ. However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and α. The first phase transition takes place with decreasing pancake-stack separation a at a = [1 – 2]λJ, and rather wide range of the ratio α, 0.4 ≲ α ≲ 0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices, a ∼ [20 – 30]λJ, and only when α exceeds a certain critical value ∼ 0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.