  We present the first measurement of elliptic ($v_2$) and triangular ($v_3$)
flow in high-multiplicity $^{3}$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$
GeV. Two-particle correlations, where the particles have a large separation in
pseudorapidity, are compared in $^{3}$He$+$Au and in $p$$+$$p$ collisions and
indicate that collective effects dominate the second and third Fourier
components for the correlations observed in the $^{3}$He$+$Au system. The
collective behavior is quantified in terms of elliptic $v_2$ and triangular
$v_3$ anisotropy coefficients measured with respect to their corresponding
event planes. The $v_2$ values are comparable to those previously measured in
$d$$+$Au collisions at the same nucleon-nucleon center-of-mass energy.
Comparison with various theoretical predictions are made, including to models
where the hot spots created by the impact of the three $^{3}$He nucleons on the
Au nucleus expand hydrodynamically to generate the triangular flow. The
agreement of these models with data may indicate the formation of low-viscosity
quark-gluon plasma even in these small collision systems.
