We report the spontaneous formation of a characteristic periodic pattern through the phase separation of a tripolymer solution comprising polyethylene-glycol (PEG)/dextran (DEX)/gelatin. When this tripolymer solution is introduced into a glass capillary with a PEG-coated inner surface, we observe the time-dependent growth of microphase separation. Remarkably, a self-organized, periodic alignment of DEX- and gelatin-rich microdroplets ensues, surrounded by a PEG-rich phase. This pattern demonstrates considerable stability, enduring for at least 8 h. The fundamental characteristics of the experimentally observed periodic alignment are successfully replicated via numerical simulations using a Cahn-Hilliard model underpinned by a set of simple, theoretically derived equations. We propose that this type of kinetically stabilized periodic patterning can be produced across a broad range of phase-separation systems by selecting appropriate boundary conditions such as at the surface within a narrow channel.