We present the first evidence of low-frequency earthquakes (LFEs) associated with the deep extension of the transpressional Alpine Fault beneath the central Southern Alps of New Zealand. Our database comprises a temporally continuous 36 month-long catalog of 8760 LFEs within 14 families. To generate this catalog, we first identify 14 primary template LFEs within known periods of seismic tremor and use these templates to detect similar events in an iterative stacking and cross-correlation routine. The hypocentres of 12 of the 14 LFE families lie within 10 km of the inferred location of the Alpine Fault at depths of approximately 20-30 km, in a zone of high P-wave attenuation, low P-wave speeds, and high seismic reflectivity. The LFE catalog consists of persistent, discrete events punctuated by swarm-like bursts of activity associated with previously and newly identified tremor periods. The magnitudes of the LFEs range between M L -0.8 and M L 1.8, with an average of M L 0.5. We find that the frequency-magnitude distribution of the LFE catalog both as a whole and within individual families is not consistent with a power law, but that individual families' frequency-amplitude distributions approximate an exponential relationship, suggestive of a characteristic length-scale of failure. We interpret this LFE activity to represent quasi-continuous slip on the deep extent of the Alpine Fault, with LFEs highlighting asperities within an otherwise steadily creeping region of the fault.