Advertisers love to market their products with appeals to nature. This is because we have a twisted idea about the reality of nature whereby we think it's all harmonious, balanced, everything about nature is inherently good and so on. This false belief is described by the naturalistic fallacy or appeal to nature.
Advertisers love their buzzwords based on this fallacy. They strive to convince us that their products are healthy because they are natural, contain no additives or preservatives, they've been 'inspired by nature' (think about what that actually means - nothing!), and another ridiculous claim: that their products are 'chemical free'.
Nothing is chemical free. Everything is made of chemicals (or strictly speaking chemical elements) so it is impossible for any product to be 'chemical free'. Yet this is used as an advertising slogan or phrase and all it's used for is to deceive consumers.
As nothing is chemical free, the claim is always false - it simply cannot be true under any circumstance whatsoever. Yet, companies use it and get away with using it nonetheless.
There's a website listing some of the products that use the slogan here: http://fnochemicalfree.tumblr.com/
The chemical-free chemistry set is an amusing example and the chemical-free Miracle Gro is a particularly ridiculous example of this daft claim. Selling artificial fertilizer produced from petrochemicals under the guise of being organic (and in chemistry terms it actually is), natural and chemical-free is surely image branding taken to the extreme!
Of course, what the advertisers are relying on is people's lack of understanding about chemistry and chemicals. We've been convinced, by the advertising industry, that there's an inherent difference between 'natural' and 'synthetic' chemicals or products. So, if something is added it must be bad; and likewise, if something is removed it must be bad too - because it's no longer 'natural'. There's an excellent document produced by Sense about Science looking at claims about chemicals here: Making sense of chemical stories (PDF)
As savvy consumers we need to see through this advertising and marketing guff. The marketeers are trying (and probably succeeding) in creating a positive brand image with their appeals to nature and use of buzzwords such as 'organic', 'natural', or 'chemical free', and so charge accordingly (i.e. more) for their products; but it's mostly illusory.
Again, we're simply being taken for a ride.
A point to remember with these claims is that Deadly Nightshade (Belladonna) is 100% natural, grows wild (100% organic), and contains no additives or preservatives - but its 'goodness' doesn't quite match the myth we're being sold by the advertisers.