  Let $F$ and $H$ be $k$-uniform hypergraphs. We say $H$ is $F$-saturated if
$H$ does not contain a subgraph isomorphic to $F$, but $H+e$ does for any
hyperedge $e\not\in E(H)$. The saturation number of $F$, denoted
$\mathrm{sat}_k(n,F)$, is the minimum number of edges in a $F$-saturated
$k$-uniform hypergraph $H$ on $n$ vertices. Let $C_3^{(3)}$ denote the
$3$-uniform loose cycle on $3$ edges. In this work, we prove that
  \[
  \left(\frac{4}3+o(1)\right)n\leq \mathrm{sat}_3(n,C_3^{(3)})\leq
\frac{3}2n+O(1).
  \]
  This is the first non-trivial result on the saturation number for a fixed
short hypergraph cycle.
