  Let $H$ be an $n$-vertex 3-uniform hypergraph such that every pair of
vertices is in at least $n/3+o(n)$ edges. We show that $H$ contains two
vertex-disjoint tight paths whose union covers the vertex set of $H$. The
quantity two here is best possible and the degree condition is asymptotically
best possible. This result also has an interpretation as the \emph{deficiency
problems}, recently introduced by Nenadov, Sudakov and Wagner: every such $H$
can be made Hamiltonian by adding at most two vertices and all triples
intersecting them.
