  The detection of gravitational waves with Advanced LIGO and Advanced Virgo
has enabled novel tests of general relativity, including direct study of the
polarization of gravitational waves. While general relativity allows for only
two tensor gravitational-wave polarizations, general metric theories can
additionally predict two vector and two scalar polarizations. The polarization
of gravitational waves is encoded in the spectral shape of the stochastic
gravitational-wave background, formed by the superposition of cosmological and
individually-unresolved astrophysical sources. Using data recorded by Advanced
LIGO during its first observing run, we search for a stochastic background of
generically-polarized gravitational waves. We find no evidence for a background
of any polarization, and place the first direct bounds on the contributions of
vector and scalar polarizations to the stochastic background. Under log-uniform
priors for the energy in each polarization, we limit the energy-densities of
tensor, vector, and scalar modes at 95% credibility to $\Omega^T_0 < 5.6 \times
10^{-8}$, $\Omega^V_0 < 6.4\times 10^{-8}$, and $\Omega^S_0 < 1.1\times
10^{-7}$ at a reference frequency $f_0 = 25$ Hz.
