Photonics offers unique capabilities for quantum information processing (QIP) such as room-temperature operation, the scalability of nanophotonics, and access to ultrabroad bandwidths and consequently ultrafast operation. Ultrashort pulse sources of quantum states in nanophotonics are an important building block for achieving scalable ultrafast QIP; however, their demonstrations so far have been sparse. Here, we demonstrate a femtosecond biphoton source in dispersion-engineered periodically poled lithium niobate nanophotonics. We measure 17 THz of bandwidth for the source centered at 2.09 µm, corresponding to a few optical cycles, with a brightness of 8.8 GHz/mW. Our results open new paths toward realization of ultrafast nanophotonic QIP.