Cells are not directly accessible in vivo and therefore their mechanical properties cannot be measured by methods that require a direct contact between probe and cell. Here, we introduce a novel in vivo assay based on particle tracking microrheology whereby the extent and time-lag dependence of the mean squared displacements of thermally excited nanoparticles embedded within the cytoplasm of developing embryos reflect local viscoelastic properties. As a proof of principle, we probe local viscoelastic properties of the cytoplasm of developing Caenorhabditis elegans embryos. Our results indicate that unlike differentiated cells, the cytoplasm of these embryos does not exhibit measurable elasticity, but is highly viscous. Furthermore, the viscosity of the cytoplasm does not vary along the anterior-posterior axis of the embryo during the first cell division. These results support the hypothesis that the asymmetric positioning of the mitotic spindle stems from an asymmetric distribution of elementary force generators as opposed to asymmetric viscosity of the cytoplasm.