Two kinds of Twist Grain Boundary (TGB) phases have been observed until now: TGB-A and TGB-C, which are composed of grains, possessing the local structure of smectics A and C, respectively. According to Renn's theory, the third TGB phase may exist in the vicinity of the chiral NAG-point: the TGB-C* phase with the local smectic C* structure. We investigated several mixtures possessing chiral NAG-point. In few systems of this kind we observed two TGB phases in place of the N*AC* point. One of these phases was the TGB-A phase. The other phase exhibited textures typical for both TGB and smectic C* phases. Texture observations and light diffraction experiments suggest that the low-temperature TGB phase might have the TGB-C* structure predicted by Renn.