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Photonic integration requires a versatile packaging technology that enables low-loss interconnects between photonic chips in three-dimensional configurations. In this paper we introduce the concept of photonic wire bonding, where polymer waveguides with three-dimensional freeform geometries are used to bridge the gap between nanophotonic circuits located on different chips. In a proof-of-principle experiment, we demonstrate the fabrication of single-mode photonic wire bonds (PWB) by direct-write two-photon lithography. First-generation prototypes allow for efficient broadband coupling with average insertion losses of only 1.6 dB in the C-band and can carry wavelength-division multiplexing signals with multi-Tbit/s data rates. Photonic wire bonding is well suited for automated mass production, and we expect the technology to enable optical multi-chip systems with enhanced performance and flexibility.