Despite the rapid and great developments in the field of 3D hydrogel printing, a major ongoing challenge is represented by the development of new processable materials that can be effectively used for bioink formulation. In this work, we present an approach to 3D deposit, a new class of fully-synthetic, biocompatible PolyIsoCyanide (PIC) hydrogels that exhibit a reverse gelation temperature close to physiological conditions (37 °C). Being fully-synthetic, PIC hydrogels are particularly attractive for tissue engineering, as their properties—such as hydrogel stiffness, polymer solubility, and gelation kinetics—can be precisely tailored according to process requirements. Here, for the first time, we demonstrate the feasibility of both 3D printing PIC hydrogels and of creating dual PIC-Gelatin MethAcrylate (GelMA) hydrogel systems. Furthermore, we propose the use of PIC as fugitive hydrogel to template structures within GelMA hydrogels. The presented approach represents a robust and valid alternative to other commercial thermosensitive systems—such as those based on Pluronic F127—for the fabrication of 3D hydrogels through additive manufacturing technologies to be used as advanced platforms in tissue engineering.