Low-phase-noise microwave oscillators are important to a wide range of subjects, including communications, radar and metrology. Photonic-based microwave-wave sources now provide record, close-to-carrier phase-noise performance, and compact sources using microcavities are available commercially. Photonics-based solutions address a challenging scaling problem in electronics, increasing attenuation with frequency. A second scaling challenge, however, is to maintain low phase noise in reduced form factor and even integrated systems. On this second front, there has been remarkable progress in the area of microcavity devices with large storage time (high optical quality factor). Here we report generation of highly coherent microwaves using a chip-based device that derives stability from high optical quality factor. The device has a record low electronic white-phase-noise floor for a microcavity-based oscillator and is used as the optical, voltage-controlled oscillator in the first demonstration of a photonic-based, microwave frequency synthesizer. The synthesizer performance is comparable to mid-range commercial devices.