The PHANGS collaboration has been building a reference data set for the multiscale, multiphase study of star formation and the interstellar medium (ISM) in nearby galaxies. With the successful launch and commissioning of JWST, we can now obtain high-resolution infrared imaging to probe the youngest stellar populations and dust emission on the scales of star clusters and molecular clouds (similar to 5-50 pc). In Cycle 1, PHANGS is conducting an eight-band imaging survey from 2 to 21 mu m of 19 nearby spiral galaxies. Optical integral field spectroscopy, CO(2-1) mapping, and UV-optical imaging for all 19 galaxies have been obtained through large programs with ALMA, VLT-MUSE, and Hubble. PHANGS-JWST enables a full inventory of star formation, accurate measurement of the mass and age of star clusters, identification of the youngest embedded stellar populations, and characterization of the physical state of small dust grains. When combined with Hubble catalogs of similar to 10,000 star clusters, MUSE spectroscopic mapping of similar to 20,000 H ii regions, and similar to 12,000 ALMA-identified molecular clouds, it becomes possible to measure the timescales and efficiencies of the earliest phases of star formation and feedback, build an empirical model of the dependence of small dust grain properties on local ISM conditions, and test our understanding of how dust-reprocessed starlight traces star formation activity, all across a diversity of galactic environments. Here we describe the PHANGS-JWST Treasury survey, present the remarkable imaging obtained in the first few months of science operations, and provide context for the initial results presented in the first series of PHANGS-JWST publications.