I heard that there is a theorem due to Rosenlicht which says the following:

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**Theorem.** Let $X$ be a complex projective manifold and $V$ a non-trivial holomorphic vector field on $X$. Then $X$ is uniruled,ie,can be covered by rational curves,if $V$ has a zero.

I have thought for a few days and failed to give myself a proof. Can somebody give me the reference or say something about the idea of proof?

Thanks in advance.