  We prove a Chung-type law of the iterated logarithm for a multiparameter
extension of the fractional Brownian motion which is not increment stationary.
This multiparameter fractional Brownian motion behaves very differently at the
origin and away from the axes, which also appears in the Hausdorff dimension of
its range and in the measure of its pointwise H\"older exponents. A functional
version of this Chung-type law is also provided.
