  Given a hypergraph $H$, the size-Ramsey number $\hat{r}_2(H)$ is the smallest
integer $m$ such that there exists a graph $G$ with $m$ edges with the property
that in any colouring of the edges of $G$ with two colours there is a
monochromatic copy of $H$. We prove that the size-Ramsey number of the
$3$-uniform tight path on $n$ vertices $P^{(3)}_n$ is linear in $n$, i.e.,
$\hat{r}_2(P^{(3)}_n) = O(n)$. This answers a question by Dudek, Fleur, Mubayi,
and R\"odl for $3$-uniform hypergraphs [On the size-Ramsey number of
hypergraphs, J. Graph Theory 86 (2016), 417-434], who proved
$\hat{r}_2(P^{(3)}_n) = O(n^{3/2} \log^{3/2} n)$.
