The structure of MX₃ transition metal trichalcogenides (TMTs, with M a transition metal and X a chalcogen) is typified by one-dimensional (1D) chains weakly bound together via van der Waals interactions. This structural motif is common across a range of M and X atoms (e.g., NbSe₃, HfTe_3,TaS₃), but not all M and X combinations are stable. We report here that three new members of the MX₃ family which are not stable in bulk, specifically NbTe₃, VTe₃, and TiTe₃, can be synthesized in the few- (2-4) to single-chain limit via nanoconfined growth within the stabilizing cavity of multiwalled carbon nanotubes. Transmission electron microscopy (TEM) and atomic-resolution scanning transmission electron microscopy (STEM) reveal the chain-like nature and the detailed atomic structure. The synthesized materials exhibit behavior unique to few-chain quasi-1D structures, such as few-chain spiraling and a trigonal antiprismatic rocking distortion in the single-chain limit. Density functional theory (DFT) calculations provide insight into the crystal structure and stability of the materials, as well as their electronic structure.