The Heckscher-Ohlin model predicts that trade openness causes the skill premium to increase in skill-abundant developed countries, and to decrease in skill-scarce developing countries. Empirical evidence, however, shows that the skill premium declined in some developing countries, while others experienced an increase in wage inequality. This paper develops a North-South model, where firms produce a low-skilled and a high-skilled intensive good. The production of a unit of either good involves a continuum of L-tasks and H-tasks. The L-tasks can be performed by low-skilled workers, and the H-tasks can be performed by high-skilled workers. The Northern firms can produce the task in their headquarters, or offshore the task to the South. The results of the model suggest there is a threshold skill abundance level in the South, above which countries experience an increase in the skill premium after an improvement in the offshoring technology, and below which countries experience a decrease in the skill premium. The same pattern occurs with an improvement in the offshoring technology of tasks in the high-skilled and the low-skilled intensive industries. If wages in local production catch up with wages in the offshoring sector, offshoring does not impact wage inequality at a certain level of skill abundance. A threshold estimation, on 29 developing countries over the period 1982-2000, shows that there is a statistically significant skill abundance threshold, below which the coefficient on the relationship between offshoring and wage inequality is negative, and above which there is no impact of offshoring on wage inequality. Similar results are reached if offshoring is replaced by variables that proxy for the offshoring technology.