In 1946, Chung and Fuchs proved a theorem that provides a sufficient condition for the law of the iterated logarithm (LIL) to hold.
I believe you're referring to the Chung's probability theorem, also known as Chung's lemma. However, I think you might be looking for the Chung-Fuchs theorem or more specifically, the probability density function (pdf) related to Chung's work. chung probability pdf
$$ f_{\text{Chung}}(x) = \frac{1}{2\sqrt{2\pi}}\frac{1}{x^{\frac{3}{2}}} \exp\left( - \frac{1}{2x} \right) $$ for $x>0$ In 1946, Chung and Fuchs proved a theorem