The equilibrium reaction is:
\[ \text{Cr}_2\text{O}_7^{2-} + [\text{H}^+] + \text{OH}^- \rightleftharpoons 2\text{CrO}_4^{2-}. \]
In a basic medium (OH$^-$), the reaction shifts to the right to produce more CrO$_4^{2-}$, as OH$^-$ consumes H$^+$, reducing its concentration. Conversely, in an acidic medium (H$^+$), the equilibrium shifts to the left, favoring Cr$_2$O$_7^{2-}$.
Thus, the equilibrium shifts to the right in a basic medium.