  During its two year prime mission the Transiting Exoplanet Survey Satellite
(TESS) will perform a time-series photometric survey covering over 80% of the
sky. This survey comprises observations of 26 24 x 96 degree sectors that are
each monitored continuously for approximately 27 days. The main goal of TESS is
to find transiting planets around 200,000 pre-selected stars for which fixed
aperture photometry is recorded every two minutes. However, TESS is also
recording and delivering Full-Frame Images (FFIs) of each detector at a 30
minute cadence. We have created an open-source tool, eleanor, to produce light
curves for objects in the TESS FFIs. Here, we describe the methods used in
eleanor to produce light curves that are optimized for planet searches. The
tool performs background subtraction, aperture and PSF photometry,
decorrelation of instrument systematics, and cotrending using principal
component analysis. We recover known transiting exoplanets in the FFIs to
validate the pipeline and perform a limited search for new planet candidates in
Sector 1. Our tests indicate that eleanor produces light curves with
significantly less scatter than other tools that have been used in the
literature. Cadence-stacked images, and raw and detrended eleanor light curves
for each analyzed star will be hosted on MAST, with planet candidates on
ExoFOP-TESS as Community TESS Objects of Interest (CTOIs). This work confirms
the promise that the TESS FFIs will enable the detection of thousands of new
exoplanets and a broad range of time domain astrophysics.
