  We establish a Chung-type law of the iterated logarithm for the solutions of
a class of stochastic heat equations driven by a multiplicative noise whose
coefficient depends on the solution, and this dependence takes us away from
Gaussian setting. Based on the literature on small ball probabilities and the
technique of freezing coefficients, the limiting constant in Chung's law of the
iterated logarithm can be evaluated almost surely.
