Polystyrene(commonly known as Styrofoam) cups are extremely harmful to the environment. Not only are they harmful to produce...

...A 1986 EPA report on solid waste named the polystyrene manufacturing process as the 5th largest creator of hazardous waste.

The National Bureau of Standards Center for Fire Research identified 57 chemical byproducts released during the combustion of polystyrene foam. The process of making polystyrene pollutes the air and creates large amounts of liquid and solid waste. These products are also made with petroleum, a non-sustainable and heavily polluting resource.
The use of hydrocarbons in polystyrene foam manufacturing releases the hydrocarbons into the air at ground level; there, combined with nitrogen oxides in the presence of sunlight, they form tropospheric ozone -- a serious air pollutant at ground level. According to the EPA (U.S. Environmental Protection Agency) more than 100 million Americans currently live in areas that fail to meet air quality standards for ozone. California, the Texas Gulf Coast, the Chicago-Milwaukee area, and the Northeastern U.S. all have "serious ozone air quality problems," according to EPA. Ozone is definitely a dangerous pollutant. The EPA says: "Healthy individuals who are exercising while ozone levels are at or only slightly above the standard can experience reduced functioning of the lungs, leading to chest pain, coughing, wheezing, and pulmonary congestion. In animal studies, long-term exposure to high levels of ozone has produced permanent structural damage to animal lungs while both short and long term exposure has been found to decrease the animal's capability to fight infection." In other words, prolonged exposure to atmospheric ozone above legal limits might be expected to damage the immune system.
Extruded polystyrene is usually made with hydro-fluorocarbons (HFC-134a), which have global warming potentials of approximately 1000–1300 times that of carbon dioxide(However extruded is not used in food products)...

...But also releases toxic chemicals within the process of degradation which can take hundreds of years. This causes another problem: Ocean and landfill choking litter. We didn't start producing polystyrene foam until relatively recently, if we keep producing it in mass quantities, it will be lining our streets in a matter of decades...

...Polystyrene foam is often dumped into the environment as litter. This material is notorious for breaking up into pieces that choke animals and clog their digestive systems.
By volume, the amount of space used up in landfills by all plastics is between 25 and 30 percent. -"Polystyrene Fact Sheet," Foundation for Advancements in Science and Education.

The United Nations Environment Program estimated in 2006 that every square mile of ocean hosts 46,000 pieces of floating plastic.

Chick-Fil-A Now has a campaign to bring recycling receptacles for their polystyrene cups within their restaurant.
These are FAQs from their own website:
Q: What recycling options does Chick-Fil-A have available for cups or plastic bottles in its Restaurants?
A: While we do not have a company-wide uniform solution for recycling at this time, Chick-Fil-A is currently researching and looking into recycling options. Chick-Fil-A began testing in-Restaurant recycling in 2011

Q: Is Chick-Fil-A going to change to an alternative cup?
A: We continually receive positive customer feedback on the insulating properties of our cups. Research also shows our foam cup is surprisingly easier on the environment than current alternatives. We concluded that no other cup serves our customers as well as the foam cup.

One thing that makes our current cups stand out is that they are recyclable where collection is available. To demonstrate our commitment to both the environment and the communities we serve, we have collaborated with foam recycling facilities and transport companies to pioneer a recycling network.

Currently, our home office and 90 Chick-fil-A Restaurants are equipped to recycle the cups, with a goal of 400 Restaurants participating by the end of 2013 and chain wide during the next few years.

I think we can all respect the initiative(albeit quite late in the game) that Chick-Fil-A is taking to improve their environmental impact, but I think you would join me in saying, “This is not enough!” It’s not enough for Chick-Fil-A to lazily invest in bandage solution recycling programs, which by the way, exist only in-restaurant.
Let me ask you, how many people do you think use the drive-thru? Do you think they are going to return to the chik-fil-a to say, ”Hey, recycle my cups.”
How about people who order “To Go”?
The sad fact is that most recycling centers and pickup services won’t accept polystyrene so it ends up in a land-fill or god-forbid, the ocean. This means that virtually the only recycling that’s going to get done is by those who choose to eat inside the restaurant or the employees themselves.
As the facts above(as well as many others not cited here) show, the continued MASS PRODUCTION of polystyrene foam cups specifically for Chick-Fil-A is the real problem that Chick-Fil-A simply doesn’t want to solve or be solved as their Q&A shows, because apparently keeping my lemonade cold is more important than progressive industry or an environmental consciousness.

So please, Despite how you may feel about Chick-Fil-A's position on social issues, this one goes beyond social into an environmental one that will negatively affect us in the future regardless of your income level, race, sex or creed.

Chik-Fil-A Executive Committee
S. Truett Cathy, Founder, Chairman and Chief Executive Officer
Dan T. Cathy, President and Chief Operating Officer
Donald M. "Bubba" Cathy, Executive Vice President and Dwarf House President
James "Buck" McCabe, Executive Vice President, Finance and Chief Financial Officer
Steve Robinson, Executive Vice President, Chief Marketing Officer
Perry Ragsdale, Executive Vice President, Design, and Construction
Timothy Tassopoulos, Executive Vice President, Operations
Headquarters
Chick-fil-A, Inc.
5200 Buffington Road
Atlanta, GA 30349-2998
(404) 765-8038
www.chick-fil-a.com
www.chick-fil-a.com/pressroom
www.cathyfamily.com

1-866-232-2040 (customer feedback line).