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Given surjective homomorphisms $R\\to T\\gets S$ of local rings, and ideals in $R$ and $S$ that are isomorphic to some $T$-module $V$, the \\emph{connected sum} $R#_TS$ is defined to be the local ring obtained by factoring out the diagonal image of $V$ in the fiber product $R\\times_TS$. When $T$ is Cohen-Macaulay of dimension $d$ and $V$ is a canonical module of $T$, it is proved that if $R$ and $S$ are Gorenstein of dimension $d$, then so is $R#_TS$. 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