A one-dimensional coupled chemistry and flow model of the earth's atmosphere is used to study the relationship between ozone content and oxygen level. The effects of the biogenic trace gases methane and nitrous oxide are considered, as well as the production of odd nitrogen in lightning discharges. The ozone column depth is found to increase monotonically with increasing oxygen content, in contrast with previous predictions that the column depth should peak at ~10-1 PAL (present atmospheric level) of O2. The critical O2 level at which an effective ultraviolet shield is produced is in the neighborhood of 10-1 PAL. Implications of this result for the emergence of terrestrial land life are considered.