  We present the first Advanced LIGO and Advanced Virgo search for ultracompact
binary systems with component masses between 0.2 $M_\odot$ - 1.0 $M_\odot$
using data taken between September 12, 2015 and January 19, 2016. We find no
viable gravitational wave candidates. Our null result constrains the
coalescence rate of monochromatic (delta function) distributions of
non-spinning (0.2 $M_\odot$, 0.2 $M_\odot$) ultracompact binaries to be less
than $1.0 \times 10^6 \text{Gpc}^{-3} \text{yr}^{-1}$ and the coalescence rate
of a similar distribution of (1.0 $M_\odot$, 1.0 $M_\odot$) ultracompact
binaries to be less than $1.9 \times 10^4 \text{Gpc}^{-3} \text{yr}^{-1}$ (at
90 percent confidence). Neither black holes nor neutron stars are expected to
form below ~ 1 solar mass through conventional stellar evolution, though it has
been proposed that similarly low mass black holes could be formed primordially
through density fluctuations in the early universe. Under a particular
primordial black hole binary formation scenario, we constrain monochromatic
primordial black hole populations of 0.2 $M_\odot$ to be less than $33\%$ of
the total dark matter density and monochromatic populations of 1.0 $M_\odot$ to
be less than $5\%$ of the dark matter density. The latter strengthens the
presently placed bounds from micro-lensing surveys of MAssive Compact Halo
Objects (MACHOs) provided by the MACHO and EROS collaborations.
