Isotope-shift spectroscopy with narrow optical transitions provides a benchmark for atomic structure calculations and has also been proposed as a way to constrain theories predicting physics beyond the standard model. Here we measure frequency shifts of the 1 S 0 → 3 P 1 and 1 S 0 → 3 P 0 transitions between 84Sr,86Sr, and 87Sr, relative to 88Sr. Using the isotope-shift measurements of the two transitions, a King plot analysis is performed, revealing a nonlinearity in the measured values.