Why not use radio buttons instead? They work this way by default - only one can be selected at a time.
But sure, you can do this with conditional formatting. On Checkbox 2 &3, have conditional formatting that disables them if 1 is equal to true. On Checkbox 1 & 2, have conditional formatting that disables them if 3 is equal to true. On Checkbox 1 & 3, have conditional formatting that disables them if 2 is equal to true.