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Acoustic devices play an important role in classical information processing. The slower speed and lower losses of mechanical waves enable compact and efficient elements for delaying, filtering, and storing of electric signals at radio and microwave frequencies. Discovering ways of better controlling the propagation of phonons on a chip is an important step towards enabling larger-scale phononic circuits and systems. We present a platform, inspired by decades of advances in integrated photonics, that utilizes the strong piezoelectric effect in a thin film of lithium niobate on sapphire to excite guided acoustic waves immune from leakage into the bulk due to the phononic analogue of index guiding. We demonstrate an efficient transducer matched to 50 Ω and guiding within a 1 μ m wide mechanical waveguide as key building blocks of this platform. Putting these components together, we realize acoustic delay lines …