We present the JWST cycle 1 53.8 h medium program FRESCO, short for ‘First Reionization Epoch Spectroscopically Complete Observations’. FRESCO covers 62 arcmin2 in each of the two GOODS/CANDELS fields for a total area of 124 arcmin2 exploiting JWST’s powerful new grism spectroscopic capabilities at near-infrared wavelengths. By obtaining ∼2 h deep NIRCam/grism observations with the F444W filter, FRESCO yields unprecedented spectra at R ∼ 1600 covering 3.8–5.0 µm for most galaxies in the NIRCam field of view. This setup enables emission line measurements over most of cosmic history, from strong PAH lines at z ∼ 0.2–0.5, to Pa α and Pa β at z ∼ 1–3, He i and [S iii] at z ∼ 2.5–4.5, H α and [N ii] at z ∼ 5–6.5, up to [O iii] and H β for z ∼ 7–9 galaxies. FRESCO’s grism observations provide total line fluxes for accurately estimating galaxy stellar masses and calibrating slit-loss corrections of NIRSpec/MSA spectra in the same field. Additionally, FRESCO results in a mosaic of F182M, F210M, and F444W imaging in the same fields to a depth of ∼28.2 mag (5σ in 0${_{.}^{\prime\prime}}$32 diameter apertures). Here, we describe the overall survey design and the key science goals that can be addressed with FRESCO. We also highlight several, early science results, including: spectroscopic redshifts of Lyman break galaxies that were identified almost 20 yr ago, the discovery of broad-line active galactic nuclei at z > 4, and resolved Pa α maps of galaxies at z ∼ 1.4. These results demonstrate the enormous power for serendipitous discovery of NIRCam/grism observations.