The endosperm is at the center of successful seed formation in flowering plants. Being itself a product of fertilization, it is devoted to nourish the developing embryo and typically possesses a triploid genome consisting of two maternal and one paternal genome complement. Interestingly, endosperm development is controlled by epigenetic mechanisms conferring parent-of-origin-dependent effects that influence seed development. In the model plant Arabidopsis thaliana, we have previously described an endosperm-specific heterochromatin fraction, which increases with higher maternal, but not paternal, genome dosage. Here, we report a detailed analysis of chromosomal arrangement and association frequency in endosperm nuclei. We found that centromeric FISH signals in isolated nuclei show a planar alignment that may results from a semi-rigid, connective structure between chromosomes. Importantly, we found frequent pairwise association of centromeres, chromosomal segments, and entire arms of chromosomes in 3C endosperm nuclei. These associations deviate from random expectations predicted by numerical simulations. Therefore, we suggest a non-random chromosomal organization in the triploid nuclei of Arabidopsis endosperm. This contrasts with the prevailing random arrangement of chromosome territories in somatic nuclei. Based on observations on a series of nuclei with varying parental genome ratios, we propose a model where chromosomes associate pairwise involving one maternal and one paternal complement. The functional implications of this predicted chromosomal arrangement are discussed.