Solution:

We can write $$\frac{1}{20^{20}}=\frac{1}{(4\cdot5)^{20}}=\frac{5^{20}}{10^{40}}.$$ Now $5^{20}=95{,}367{,}431{,}640{,}625$, which has $14$ digits and begins with $9$. Dividing by $10^{40}$ places this 14-digit number after the decimal point with $40-14=26$ zeros before the first digit.

Thus, the correct answer is D .