Eggs start in the ovary. During ovulation, the yolk is released into the oviduct. After, the yolk goes through the oviduct, where it is fertilized (in case of a rooster is present) and the egg white is deposited.
When the egg moves in the uterus, the yolk is encapsulated in the pod, after the shell is colored, and the bloom adhered. Finally, the egg continues through the uterus to be laid. It takes 24 to 26 hours to implement this process.
Can chickens lay 3 eggs in a day?
Two eggs from one chicken in one day is rare, three seems not possible. If you espied three eggs from one chicken, you should elicit this. You may have had two chickens in the nest or you also may have forgotten to collect eggs from the day before – or missed one, or can your hen have laid an egg after you collected them.
How many eggs may a chicken lay in one day?
One egg
Besides, because the hens usually reproductive system is sensitive to light exposure, finally the hen will lay too late in a day for its body to begin forming a new egg. Then, the hens will skip a day or more before laying again.
Two or more eggs
Sometimes, chickens will release two yolks at the same time. This is normal with young hens who are maturing. Often, these two yolks are encapsulated in one double yolk egg. However, a hen still may lay two eggs in one day.
Further reading: Can a chicken lay 2 eggs a day?

What are the factors affecting laying?
Apart from lighting, there are a number of reasons to lay chicken including molting and age that can reduce or prevent egg production.
First, it is poor nutrition. If a hen is not receiving suitable amounts of feed, or if an imbalance happens as they provide too much or too little salt, these also make hens unable to lay eggs. Besides, the chickens also must receive adequate amounts of minerals, and vitamins.
Furthermore, if feed is not stored properly, molds may grow on it. These can release toxins which affect the health of hens and can prevent laying. Hens raised in backyards can also eat objects that are not part of their feed as seeds of toxic plants, and these may be harmful.
On the other hand, external parasites — such as mites, lice, fleas and external parasites — such as tapeworms or roundworms also may affect laying.
Finally, stress is also one of the causes of reduction in egg production.

When a chicken lays eggs?
A hen starts to lay eggs, when they reach from 18 to 20 weeks of age. About the timing of oviposition, it varies with a chicken’s breed and depends on how much light exposure hens get. Commonly, It is best for chickens to lay an egg in the morning, or between 2 and 6 hours after sun up.
What is the effect of exposure light to lay chicken?
A chicken’s reproductive cycle is usually controlled by a photo-period. It is known as the length of time when it is exposed to daylight above a specific level therefore is governed by the seasons in nature.
Hens need at least 12 hours of light per day to produce eggs and have a high production rate for eggs at 16 hours of daylight. Besides, they also can lay eggs with as little as 8 hours of daylight, however it is a great deal fewer eggs, sometimes from 2 to 3 a week. I keep
Maybe you don’t know, hens often lay eggs within six hours of sunrise which is why commercially hens are provided at least 16 hours of daylight, even if it is artificial light. This helps to fool their systems into thinking it is summer all the time, so they keep laying at max rate.
Unless Hens are not exposed to artificial lighting in the coop, they will stop laying eggs until late fall for about two months. They start laying again in late winter.
What is the difference about the lay period between chicken genes?
Able to lay chicken also depends mostly on breeds. Some breeds of chicken are known to lay better than others as White Leghorn or Rhode Island Red lay 20 in a week, almost 5 per week. They also can gain from 250 to 300 eggs in one year.
In which, brown-egg breeds tend to lay sooner in the day. Because brown egg layers follow a rule lay far fewer eggs than their lighter egged cousins.
Besides, White and blue or green egg breeds tend to lay later in the day.
Moreover, hybrids are mated to be producers and also have been carefully selected so they usually have a shorter egg cycle and in some cases, they can lay an egg a day.
Broilers also are known to lay fewer eggs than laying hens. Maybe it depends on the useful value.
So, to select a good breed, in many cases, you can go to a feed store to buy. Some of them are Buff Orpingtons, Production Reds, Easter Eggers, Australorps,…
Conclusion
So, can a chicken lay 3 eggs in one day? Unless mutation, it seems not possible.
However, to create a high value for producing eggs, you should notice exposure to light, nutrition and harmful feed to keep health for your hens.
Taking care of the breed also is a value method to choose a good breed.