We prove a Chung-type law of the iterated logarithm for a multiparameter extension of the frac-tional Brownian motion which is not increment stationary. This multiparameter fractional Brow-nian 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 Hölder exponents. A functional version of this Chung-type law is also provided.