  A well-known theorem of Erd\H{o}s and Gallai asserts that a graph with no
path of length $k$ contains at most $\frac{1}{2}(k-1)n$ edges. Recently
Gy\H{o}ri, Katona and Lemons gave an extension of this result to hypergraphs by
determining the maximum number of hyperedges in an $r$-uniform hypergraph
containing no Berge path of length $k$ for all values of $r$ and $k$ except for
$k=r+1$. We settle the remaining case by proving that an $r$-uniform hypergraph
with more than $n$ hyperedges must contain a Berge path of length $r+1$.
