  We study a one-dimensional gas of $N$ Brownian particles that diffuse
independently, but are {\it simultaneously} reset to the origin at a constant
rate $r$. The system approaches a non-equilibrium stationary state (NESS) with
long-range interactions induced by the simultaneous resetting. Despite the
presence of strong correlations, we show that several observables can be
computed exactly, which include the global average density, the distribution of
the position of the $k$-th rightmost particle and the spacing distribution
between two successive particles. Our analytical results are confirmed by
numerical simulations. We also discuss a possible experimental realisation of
this resetting gas using optical traps.
