Establishing the abundance of the extinct radionuclide 60Fe (half-life 2.62 Ma) in the early solar system is important for understanding the astrophysical context of solar system formation. While bulk measurements of early solar system phases show a low abundance consistent with galactic background, some in situ measurements by secondary ion mass spectrometry (SIMS) imply a higher abundance, which would require injection from a nearby supernova (SN). Here we present in situ nickel isotopic analyses by resonance ionization mass spectrometry (RIMS) in a chondrule from the primitive meteorite Semarkona (LL3.00). The same chondrule had been previously analyzed by SIMS. Despite improved precision compared to SIMS, the RIMS nickel isotopic data do not reveal any resolved excesses of 60Ni that could be unambiguously ascribed to in situ 60Fe decay. Linear regression of 60Ni/58Ni versus 56Fe/58Ni yields an initial 60Fe/56Fe ratio for this chondrule of (3.8 ± 6.9) × 10-8, which is consistent with both the low initial value found by bulk measurements and the low end of the range of initial ratios inferred from some in situ work. The same regression also gives a solar initial 60Ni/58Ni ratio, which shows that this sample was not disturbed by nickel mobilization, thus agreeing with a low initial 60Fe/56Fe ratio. These findings agree with a re-evaluation of previous SIMS measurements of the same sample. Supernova injection of 60Fe into the solar system or its parental cloud material is therefore not necessary to account for the measured solar system’s initial amount of 60Fe.