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Let $k$ and $m$ be positive integers. A collection of $k$-multisets from$\{1,..., m \}$ is intersecting if every pair of multisets from the collectionis intersecting. We prove that for $m \geq k+1$, the size of the largest suchcollection is $\binom{m+k-2}{k-1}$ and that when $m > k+1$, only a collectionof all the $k$-multisets containing a fixed element will attain this bound. Thesize and structure of the largest intersecting collection of $k$-multisets for$m \leq k$ is also given.

An Erd\H{o}s-Ko-Rado theorem for multisets