system
Given the following post, respond as if you're commenting on Reddit:
human
If babies breathe through the umbilical cord, how do chicks breathe in eggs ?
gpt
It's predominately diffusion across the eggshell.

>...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. Rahn H, Paganelli CV, Ar A.  J Exp Zool Suppl. 1987;1:165-72.

There's ample gas diffusion across the eggshell during most of the chick's development; the eggshell itself offers little resistance to gas exchange:

>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. Jacopo P. Mortola.  Comparative Biochemistry and Physiology, Part A 153 (2009) 359–377 

Most of the resistance is from the membranes on the inside of the shell, and this resistance is reduced during development to keep pace with the increased requirements.

Very near the end of development, the chick can gain extra air through the air sac (the "internal pipping" mentioned above); but note, the air in the air sac also gets there through diffusion through the egg shell, during earlier development.   

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. Monge CC, Ostojic H, Aguilar R, Cifuentes V. Biol Res. 2000;33(3-4):209-14.)