We have observed Feshbach resonances in elastic collisions between ultracold ${}^{52}$Cr atoms. This is the first observation of collisional Feshbach resonances in an atomic species with more than one valence electron. The zero nuclear spin of ${}^{52}$Cr and thus the absence of a Fermi-contact interaction leads to regularly-spaced resonance sequences. By comparing resonance positions with multi-channel scattering calculations we determine the s-wave scattering length of the lowest $^{2S+1}Sigma_{g}^{+}$ potentials to be $unit[112(14)]{a_0}$, $unit[58(6)]{a_0}$ and $-unit[7(20)]{a_0}$ for S=6, 4, and 2, respectively, where $a_{0}=unit[0.0529]{nm}$.