ASTERIA (Arcsecond Space Telescope Enabling Research In Astrophysics) is a 6U CubeSat space telescope (10 cm x 20 cm x 30 cm, 10 kg). ASTERIAs primary mission objective was demonstrating two key technologies for reducing systematic noise in photometric observations: high-precision pointing control and high-stabilty thermal control. ASTERIA demonstrated 0.5 arcsecond RMS pointing stability and $pm$10 milliKelvin thermal control of its camera payload during its primary mission, a significant improvement in pointing and thermal performance compared to other spacecraft in ASTERIAs size and mass class. ASTERIA launched in August 2017 and deployed from the International Space Station (ISS) November 2017. During the prime mission (November 2017 -- February 2018) and the first extended mission that followed (March 2018 - May 2018), ASTERIA conducted opportunistic science observations which included collection of photometric data on 55 Cancri, a nearby exoplanetary system with a super-Earth transiting planet. The 55 Cancri data were reduced using a custom pipeline to correct CMOS detector column-dependent gain variations. A Markov Chain Monte Carlo (MCMC) approach was used to simultaneously detrend the photometry using a simple baseline model and fit a transit model. ASTERIA made a marginal detection of the known transiting exoplanet 55 Cancri e ($sim2$~Rearth), measuring a transit depth of $374pm170$ ppm. This is the first detection of an exoplanet transit by a CubeSat. The successful detection of super-Earth 55 Cancri e demonstrates that small, inexpensive spacecraft can deliver high-precision photometric measurements.