  Investigating the atmospheres of rocky exoplanets is key to performing
comparative planetology between these worlds and the terrestrial planets that
reside in the inner solar system. Terrestrial exoplanet atmospheres exhibit
weak signals, and attempting to detect them pushes at the boundaries of what is
possible for current instrumentation. We focus on the habitable-zone
terrestrial exoplanet LHS 1140b. Given its 25-day orbital period and 2 hr
transit duration, capturing transits of LHS 1140b is challenging. We observed
two transits of this object, approximately 1 yr apart, which yielded four data
sets thanks to our simultaneous use of the IMACS and LDSS3C multiobject
spectrographs mounted on the twin Magellan telescopes at Las Campanas
Observatory. We present a jointly fit white light curve, as well as jointly fit
20 nm wavelength-binned light curves from which we construct a transmission
spectrum. Binning the joint white light-curve residuals to 3-minute time bins
gives an rms of 145 ppm; binning down to 10-minute time bins gives an rms of 77
ppm. Our median uncertainty in Rp^2/Rs^2 in the 20 nm wavelength bins is 260
ppm, and we achieve an average precision of 1.3x the photon noise when fitting
the wavelength-binned light curves with a Gaussian process regression. Our
precision on Rp^2/Rs^2 is a factor of four larger than the feature amplitudes
of a clear, hydrogen-dominated atmosphere, meaning that we are not able to test
realistic models of LHS 1140b's atmosphere. The techniques and caveats
presented here are applicable to the growing sample of terrestrial worlds in
the Transiting Exoplanet Survey Satellite era, as well as to the upcoming
generation of ground-based giant segmented mirror telescopes.
