single variable is significant but overall test is not

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I do a multiple regression with 3 independent variables $X_1$, $X_2$ and $X_3$. The correlation between $Y$ and $X_1$, $Y$ and $X_2$, and $Y$ and $X_3$, are each large and statistically significant. When I fit the multiple regression, none of the t-tests on individual coefficients are significant. How could this happen?