Egg shells look as if they're solid, but in fact they're filled with tiny pores through which air can and does diffuse.
...up to the time when internal pipping takes place, when pulmonary ventilation is initiated, about 20 liters (O2 + CO2 + water vapor) have passed through 10,000 pores of an 80 gm egg.
--Pores and gas exchange of avian eggs: a review.
A typical 60-g chicken egg has about 10,000 pores, each with a functional cross section of 150–200 μm^2; therefore, the total pore area is about 1.5–2 mm^2.
--Gas exchange in avian embryos and hatchlings
You only asked about chicken eggs, but chickens have it pretty easy compared to many other avian species. For example, ostrich eggs have a much larger volume-to-surface area, meaning that exchange is less effective. One way ostriches may compensate is by incubating eggs at lower temperatures, reducing oxygen requirements; more significantly and related, incubation time is relatively slower for birds with large eggs. Birds at high altitudes have larger total pore size, adapting to the reduced O2 pressure.
Actually, a more serious problem than oxygen exchange is water exchange. The egg needs to manage water loss (not too much, not too little), and the more gas exchange the more water loss. Accordingly, birds adapted to different humidities lay eggs with different gas exchange capacities (changing pore densities for the most part); birds in very arid environments, like gulls in Chile's Atacama Desert, have very low gas and water exchange, to the point where their developing chicks are relatively hypoxic:
--Reduced oxygen diffusion across the shell of Gray gull (Larus modestus) eggs.