Ongoing antagonistic coevolution with selfish genetic elements (SGEs) can drive the evolution of host genomes. Here, we investigated whether natural variation allows some Saccharomyces cerevisiae strains to suppress their endogenous SGEs, 2-micron plasmids. 2-micron plasmids are multicopy nuclear parasites that have co-evolved with budding yeasts. To quantitatively measure plasmid stability, we developed a new Single-Cell Assay for Measuring Plasmid Retention (SCAMPR) that measures copy number heterogeneity and 2-micron plasmid loss dynamics in live cells. Next, using a survey of 52 natural S. cerevisiae isolates, we identified three strains that lack endogenous 2micron plasmids, and find that plasmid resistance is heritable. Focusing on one isolate (Y9 ragi strain), we determined that plasmid restriction is dominant and is a multigenic trait. Through Quantitative Trait Locus (QTL) mapping by bulk segregant analysis, we identified a high-confidence QTL for plasmid instability on Y9 chromosome V. We show that a single amino acid change in MMS21 is associated with increased 2-micron resistance. MMS21 encodes a SUMO E3 ligase and is an essential member of the Smc5/6 complex involved in sister chromatid cohesion, chromosome segregation, and DNA repair. Our analyses leverage standing variation in natural yeast isolates to identify a novel host determinant of plasmid stability and reveal variants in essential genes that may help hosts mitigate the fitness costs of genetic conflicts with SGEs.