High density (non-thermal-barrier) operation in the Tandem Mirror Experiment Upgrade (TMX-U) is found to be restricted by a stability limit. This limit is observed in the ratio of the neutral beam sustained central cell beta βc to the hot ion beta βih in the minimum-B anchor cells at both ends of the central cell, qualitatively consistent with a flute interchange stability limit. The ratio is βc/βih = 5, over the range of 0.03 ≤ βc ≤ 0.22, with no apparent reduction due to ballooning at high βc. This is a factor of six below the standard magnetohydrodynamic (MHD) m = 1 stability theory prediction of βc/βih = 33 at βc ≤ 0.1, where ballooning corrections to flute modes are small. The discrepancy could be due to approximations in the theory; however, experimental data indicate that the stability limit is due to drift wave turbulence or to large-m MHD flute or ballooning modes. The experimental beta limit is nearly independent of the hot electron beta in the anchor cells, which is compatible with theoretical predictions that the hot electron beta will decouple from MHD activity.