A 1 eV neutral atomic fluorine beam has been shown to produce etch rates in silicon as high as 1 mu m/min. Using a CaF2 resist layer we fabricated 120 mu m deep by 1 mu m wide trenches (aspect ratio 120:1) in silicon with little sidewall taper (slopes of about 1000:1) or aspect-ratio dependent etching effects. Achieving such anisotropic etching suggests that the scattered species do not contribute significantly to sidewall etching under the conditions of this experiment. We estimate that the ultimate depth attainable for a 1 mu m wide trench is about 250 mu m and that the critical parameter for attaining a trench of a certain depth is the aspect ratio. Our observations and analysis suggest that this etching technique can be used to fabricate trenches on a nanoscale level while maintaining high aspect ratios of 100 or greater.