Cooperative 3D printing (C3DP) is a novel approach to additive manufacturing, where multiple printhead-carrying mobile robots work cooperatively to print the desired part. The core of C3DP is the chunk-based printing strategy in which the desired part is first split into smaller chunks, and then the chunks are assigned to individual robots to print and bond. These robots will work simultaneously in a scheduled sequence to print the entire part. Although promising, C3DP lacks a generative approach that enables automatic chunking and scheduling. In this study, we aim to develop a generative approach that can automatically generate different print schedules for a chunked object by exploring a larger solution space that is often beyond the capability of human cognition. The generative approach contains 1) a random generator of diverse print schedules based on an adjacency matrix that represents a directed dependency tree structure of chunks; 2) a set of geometric constraints against which the randomly generated schedules will be checked for validation; and 3) a printing time evaluator for comparing the performance of all valid schedules. We demonstrate the efficacy of the generative approach using two case studies: a large simple rectangular bar and a miniature folding SUV with more complicated geometry. This study demonstrates that the generative approach can generate a large number of different print schedules for collision-free C3DP which cannot be explored solely using human heuristics. This generative approach lays the foundation for building the optimization approach of C3DP scheduling.