We study the statistical distribution of satellites around star-forming and quiescent central galaxies at 1 < z < 3 using imaging from the FourStar Galaxy Evolution Survey and the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey. The deep near-IR data select satellites down to log (M/M) > 9 at z < 3. The radial satellite distribution around centrals is consistent with a projected Navarro-Frenk-White profile. Massive quiescent centrals, log (M/M) > 10.78, have ∼2 times the number of satellites compared to star-forming centrals with a significance of 2.7σ even after accounting for differences in the centrals' stellar-mass distributions. We find no statistical difference in the satellite distributions of intermediate-mass quiescent and star-forming centrals, 10.48 < log (M/M) < 10.78. Compared to the Guo et al. semi-analytic model, the excess number of satellites indicates that quiescent centrals have halo masses 0.3 dex larger than star-forming centrals, even when the stellar-mass distributions are fixed. We use a simple toy model that relates halo mass and quenching, which roughly reproduces the observed quenched fractions and the differences in halo mass between star-forming and quenched galaxies only if galaxies have a quenching probability that increases with halo mass from ∼0 for log (Mh/M) ∼ 11 to ∼1 for log (M h/M) ∼ 13.5. A single halo-mass quenching threshold is unable to reproduce the quiescent fraction and satellite distribution of centrals. Therefore, while halo quenching may be an important mechanism, it is unlikely to be the only factor driving quenching. It remains unclear why a high fraction of centrals remain star-forming even in relatively massive halos.