  We present deep unbiased spectroscopy of the Hubble Ultra Deep Field (UDF)
carried out using the slitless grism spectroscopy mode of the Advance Camera
for Surveys on the Hubble Space Telescope (HST). The GRIsm ACS Program for
Extragalactic Science (GRAPES) achieves continuum detection as faint as
$z_{AB}=27.2$ using 40 orbits ($9.2 \times 10^4$ seconds) on HST. The data were
taken at four orientation angles to correct for the overlap of spectra. GRAPES
data provide a unique, uninterrupted, low resolution (R=100) spectral coverage
for $5500\AA < \lambda < 10500\AA$, and allow us to detect high redshift
galaxies at $4 < z < 7$ whether they have $\lya$ lines or just show the Lyman
Break, as well as find low luminosity AGNs in an unbiased fashion. This paper
describes in detail the observations and the data reduction, and examines the
quality of the extracted spectra. Subsequent papers will deal with the analysis
of the data. The extracted and calibrated GRAPES spectra will be available from
MAST at STScI.
