Abstract: Recently it has been proposed to search for particles outside the Standard Model (SM) in an intermediate mass range by means of precision isotope shift spectroscopy on narrow optical transitions. We perform such a measurement on two S → D transitions for five bosonic isotopes of Yb+ with an accuracy of ~ 300Hz, and observe a nonlinearity at the 3.3 σ level in the corresponding King plot. Such a nonlinearity can indicate physics beyond the SM, or higher-order effects within the SM. We identify the second-order field shift as the leading-order effect within the SM for Yb+. The observed nonlinearity pattern is consistent with both the second-order field shift, and with an unknown boson, but larger than expected from either source. In the future, more precise measurements on more transition available for Yb+ and Yb can be used to distinguish between effects within and outside the SM.