The scalability trends of modern semiconductor technology lead to increasingly dense multicore chips. Unfortunately, physical limitations in area, power, off-chip bandwidth, and yield constrain single-chip designs to a relatively small number of cores, beyond which scaling becomes impractical. Multi-chip designs overcome these constraints, and can reach scales impossible to realize with conventional single-chip architectures. However, to deliver commensurate performance, multi-chip architectures require a cross-chip interconnect with bandwidth, latency, and energy consumption well beyond the reach of electrical signaling. We propose Galaxy, an architecture that enables the construction of a many-core "virtual chip" by connecting multiple smaller chiplets through optical fibers. The low optical loss of fibers allows the flexible placement of chiplets, and offers simpler packaging, power, and heat requirements. At the same time, the low latency and high bandwidth density of optical signaling maintain the tight coupling of cores, allowing the virtual chip to match the performance of a single chip that is not subject to area, power, and bandwidth limitations. Our results indicate that Galaxy attains speedup of 2.2x over the best single-chip alternatives with electrical or photonic interconnects (3.4x maximum), and 2.6x smaller energy-delay product (6.8x maximum). We show that Galaxy scales to 4K cores and attains 2.5x speedup at 6x lower laser power compared to a Macrochip with silicon waveguides.