Your egg is most likely a chimera, which is essentially an organism that incorporates genetic material from more than 2 individuals in a process that I don't completely understand but which can occur even in humans.  The New England Jounal of Medicine ran an article about this a few years ago which even contained photos of a human chimera who was essentially a normal person but had a pigmentation pattern on his skin which looked exactly like a giant checkerboard! 

The shell gland secretes the brown pigments into the fluid bathing the egg surface. The fluid readily smears while still wet, which leaves marks on the eggs because once the egg dries the colour sets like a dye that persists even if the shell gets wet again.  Poultry farmers are accordingly fussy about absorptive bedding in nesting boxes. 

Eggs usually are laid big-end first, so probably the leading end of the egg is paler because it got its colour wiped off. This suggests that the young bird, its reproductive equipment barely mature, extruded the egg from the cloaca, possibly while sitting on soft material (details not supplied as yet). More likely the wet egg was forced through a tight, immature cloaca, wiping off much of the still-liquid pigment. Precise speculation would be pointless. Presumably at that point the bird became egg-bound for a while, perhaps because of being disturbed or exhausted by the resistance. The part of the egg still within the cloaca had time to achieve an undisturbed, deep colour before the cloaca relaxed. The sharp boundary between the colours is consistent with the egg being bound halfway out of the cloaca. This would be unusual, but not unlikely.

The answer probably lies in the fact that, until shortly before they are laid, hens' eggs are white. The brown pigmentation associated with breeds such as the Rhode Island Red and the Maran is a last-minute addition during egg formation and, like a fresh coat of paint, can come off surprisingly easily.

More than 90 per cent of the shell of a hen's egg comprises calcium carbonate crystals bound in a protein matrix. The shell starts to form after the egg has reached the uterus, where it stays for around 20 hours prior to being laid.

During this time, glands secrete the shell around the membranes that hold the yolk and albumen. In brown-egg-laying breeds, the cells lining the shell glands release pigmentation during the last 3 to 4 hours of shell formation. Most of the pigment is transferred to the cuticle, a waterproof membrane that surrounds the porous eggshell.

Several factors can disturb the cuticle formation process and thus pigmentation, such as ageing, viral infections - including that perennial chicken farmer's nemesis, bronchitis - and drugs such as nicarbazin, which has been widely fed to poultry to combat a disease caused by a type of protozoa. Possibly the most significant factor affecting egg pigmentation is exposure to stress during the formation of the egg.

If a flock of hens is disturbed by a fox during the night, for example, they might well lay paler eggs in the morning. The adrenaline the hens release puts egg-laying on hold and shuts down shell formation. The egg's pigmentation will be affected if the cuticle doesn't form properly.

Even if the pigmentation is laid down, there is no guarantee that it will last, as Morris Steggerda and Willard F. Hollander found in 1944 while they were studying eggs from a flock of Rhode Island Reds in the US. When they cleaned the eggs, the brown pigment occasionally came away; the harder the eggs were rubbed, the more pigment was removed. Only those shells with a glossy sheen retained their colour, suggesting their cuticles had been fully formed, with a protective layer that acted rather like the varnish on an oil painting.

As for the egg photographed by your questioner, the bird was probably disturbed while the cuticle was being formed and so the pigment, inadequately protected, was rubbed off the larger, rounder end of the egg as it was forced out.

The issue may have some significance for public health. The waterproof cuticle is the egg's defence against bacteria. As shell colour is affected by how well the cuticle forms, it also provides a visual test of how free of harmful bacteria an egg may be.

Hadrian Jeffs, Norwich, Norfolk, UK

Before an egg is laid, the hen's shell gland secretes pigment into the fluid bathing the egg's surface. The fluid smears readily, and any disturbance while the egg dries can create marks. Farmers are therefore fussy about the kind of bedding they use in nesting boxes.

Eggs usually are laid big end first. The hen that laid the egg in question may have resorted to using friction to release the partly laid egg from its cloaca, possibly by rubbing the egg against the bedding it was sitting on.

Alternatively, the hen may have paused halfway through laying, perhaps disturbed or exhausted, with the egg half-protruding from its cloaca. The part of the egg still within the cloaca had time to achieve a deep colour before the hen relaxed again, and this accounts for the sharp boundary in colouration seen in the photo. Such a scenario, though unusual, is not highly unlikely.

Jon Richfield, Somerset West, South Africa