The rare earth orthochromites are extremely interesting due to the richness of their optical, dielectric, and magnetic properties as well as due to their multiferroic properties which make them suitable materials to study in the nanoregime. However, the wet-chemical synthesis of these materials in nanosize is nontrivial. Here, we report for the first time, the detailed Raman spectra as well as magnetic and dielectric properties of chemically synthesized GdCrO3 nanoparticles of size ranging from 40 to 60 nm. The magnetic properties are dictated by competing Cr3+-Cr3+, Gd3+-Cr3+, and Gd3+-Gd3+ superexchange interactions in different temperature regions, resulting into an antiferromagnetic ordering at 167 K due to the Cr3+-Cr3+ followed by weak ferromagnetic ordering due to the onset of Cr3+-Gd3+ interactions. At lower temperature, it shows weak antiferromagnetic ordering due to Gd3+-Gd3+ interaction. Below 95 K, GdCrO3 nanoparticles showed the presence of negative magnetization due to Gd3+ and Cr3+ interactions resulting into weak ferromagnetic coupling. The Raman spectroscopy shows the characteristic Raman shifts indicating that below 450 cm(-1), Gd3+ ions play a dominant role in determining the phonon frequencies of GdCrO3, and above 450 cm(-1), the Cr+3 ions dominate. We also present for the first time the low temperature dielectric constant and loss tangent data for GdCrO3 in a broad temperature and frequency range. The dielectric constant shows a decrease in comparison to the bulk values due to the size dependent effects. It also shows a peak centered at around 320 K above which it shows a sharp decrease. The dielectric loss value in GdCrO3 nanoparticles is quite small and shows an interesting frequency dependent anomaly at lower temperature which might be due to the coupling between magnetic and dielectric order parameters.