We describe CHILI, the Chicago Instrument for Laser Ionization, a new resonance ionization mass spectrometer developed for isotopic analysis at high spatial resolution and high sensitivity of small samples like contemporary interstellar dust grains returned by the Stardust spacecraft. We explain how CHILI addresses the technical challenges associated with such analyses by pushing most technical specifications towards their physical limits. As an initial demonstration, after many years of designing and developing CHILI, we have analyzed presolar silicon carbide grains for their isotopic compositions of strontium, zirconium, and barium. Subsequently, after further technical improvements, we have used CHILI to analyze, for the first time without interference, all stable isotopes of iron and nickel simultaneously in presolar silicon carbide grains. With a special timing scheme for the ionization lasers, we separated iron and nickel isotopes in the time-of-flight spectrum such that the isobaric interference between 58Fe and 58Ni was resolved. In-depth discussion of the astrophysical implications of the presolar grain results is deferred to dedicated later publications. Here we focus on the technical aspects of CHILI, its status quo, and further developments necessary to achieve CHILI’s ultimate goals, ∼10 nm lateral resolution and 30–40% useful yield.