The 23.7 GHz ammonia (NH3) (1,1) inversion line is split into five hyperfine lines. Local Thermodynamic Equilibrium (LTE) suggests that the outer and inner pair of hyperfine lines should have exactly the same brightness. However, observations from the Australia Compact Telescope Array CAHCMC and the Green Bank Telescope RAMPS NH3 surveys of molecular clumps, show ubiquitous "hyperfine intensity anomalies," with typical intensity ratios RO/LO = 1.2 and LI/RI = 1.1. New MOLPOP radiative excitation models naturally reproduce the observed anomalies through selective radiative trapping of the overlapping far-infrared (2,1) - (1,1) hyperfine lines, but only if the linewidths are narrow (<0.8 km/s), much narrower than the observed linewidths (~2.0 km/s). Molecular clumps, therefore, must have narrow linewidths locally yet broad linewidths globally. These observations therefore rule out microturbulence (the same turbulent linewidths at all positions) in molecular clumps. Macroturbulence or large-scale flows are required to explain the observed hyperfine intensity anomalies.