The ability to slow down the propagation of light touches both fundamental aspects of light-matter interactions and practical applications in photonic communication and computation. Optical quantum interference can substantially reduce the speed of light while offering additional dramatic optical effects based on the ability to control electronic quantum states. Recent efforts are increasingly being directed towards harnessing these effects in integrated photonic structures. Here, we report the first demonstration of slow light and electromagnetically induced transparency in a self-contained, planar atomic spectroscopy chip. Using hot rubidium atoms in hollow-core waveguides, we demonstrate 44% optical transparency with a group index of 1,200, or more than sevenfold slower light than in photonic-crystal waveguides. Optical pulse delays of 16 ns with a delay-bandwidth product of 0.8 are observed. This implementation of atomic quantum state control in integrated photonic structures will enable coherent photonics at ultralow power levels.