  If recurrent novae are progenitors of Type Ia supernovae, their white dwarfs
must have masses close to the Chandrasekhar limit. The most reliable means of
determining white dwarf masses in recurrent novae is dynamically, via
radial-velocity and rotational-broadening measurements of the companion star.
Such measurements require the system to be both eclipsing and to show
absorption features from the secondary star. Prior to the work reported here,
the only dynamical mass estimate of a recurrent nova was for U Sco, which has a
white dwarf mass of 1.55 +/- 0.24 Msolar (Thoroughgood et al. 2001).
  We present new time-resolved, intermediate-resolution spectroscopy of the
eclipsing recurrent nova CI Aquilae (CI Aql) during quiescence. We find the
mass of the white dwarf to be 1.00 +/- 0.14 Msolar and the mass of the
secondary star to be 2.32 +/- 0.19 Msolar. We estimate the radius of the
secondary to be 2.07 +/- 0.06 Rsolar, implying that it is a slightly-evolved
early A-type star. The high mass ratio of q = 2.35 +/- 0.24 and the high
secondary-star mass implies that the mass transfer occurs on a thermal
timescale. We suggest that CI Aql is rapidly evolving into a supersoft X-ray
source, and ultimately may explode as a Type Ia supernova within 10 Myr.
