If there are chickens that lay more than one egg a day, they are very rare. The cites I can find indicate that most chickens will lay about one egg a day at the prime of their egg-laying production:
How many eggs does one hen lay per day?
This depends on: the time of year; the breed of the hen; the diet of the hen; the age of the hen; and, how the hen is looked after.
Most of the standard breeds of chickens that have been selected through the years for egg production will lay between 180 – 320 eggs per year for their first year of laying.
On one extreme, there are records of hens averaging an egg a day for over a year. The rate of laying tapers in the second year and beyond, until it may only take place during the spring.
Some of the breeds that haven’t been selected for egg production (selected for show, or other qualities, instead) may only lay eggs in the spring and early summer.
Appropriate feed mixtures also stimulate egg production. Provide 14 to 16 hours of light for hens to lay regularly.
One hen can only lay, at the most, seven eggs per week while most chickens lay fewer. A hen which lays one egg every day is a very good layer.
From: http://www.ruleworks.co.uk/cgi-bin/TUfaq.exe?Guide=Poultry&Category=Poultry%20-%20General#q9 (bolding mine)
Egg producing chickens have been bred for maximum egg production rather than meat yield, and can produce up to 300 eggs per year. These chickens are usually of the White Leghorn type and lay white eggs, although brown egg layers are also available. They have a mature body weight of 1.8 to 2.0 kg (four to five lb.).
Dual purpose chickens are raised in small flocks for both meat and egg production. They are smaller than commercial broilers, but reach a mature body weight of approximately 2.5 kg (5.5 lb.) for females and 3.0 kg (6.5 lb.) for males. The hens will produce 200 to 250 eggs per year. Typically, the eggs are brown. Available breeds include Rhode Island Red crossed with Barred Rock, Columbian Rock, or Light Sussex.
It looks as though one per day is the best you can expect. Biological systems are prone to having outliers far from the mean, so it's conceivable that somewhere out there is a chicken that can lay two, but that would definitely be unusual.