1. The problem is to evaluate $\frac{\log_3 1}{243}$.\n\n2. Recall that $\log_3 1$ means the power to which 3 must be raised to get 1. Since $3^0 = 1$, we have $\log_3 1 = 0$.\n\n3. Substitute this value back into the expression: $\frac{0}{243}$.\n\n4. Any number divided by a nonzero number is 0, so $\frac{0}{243} = 0$.\n\nFinal answer: $0$.