This is always a big issue when it comes to memory foam beds such as Comforpedic or iComfort not to mention the big boy Tempurpedic. The answer is that yes sometimes your new viscoelastic mattress may have a sort of chemical smell when it is first opened and put down.
This is usually due to the cleaning process the foam goes through just before packaging. If the mattress is not allowed to air out before being wrapped up it may hold the odor inside until unpacked. This should go away in a few hours to days depending on the surrounding air flow in the room.
It sometimes helps to take your shoes off and walk around on the mattress to help push the chemical stink out and this is how to get rid of the memory foam odor or smell.
While this is sometimes a complaint the out-gassing effect is usually not harmful at all but there are always some people who are extremely sensitive to all types of things. These folks may have a semi strong reaction to the stink but not really in a harmful or dangerous way.
I really don’t think your foam mattress will kill you due to the smell but I am not an expert in suspicious mattress deaths.
It also may depend on the quality of the mattress you buy. I do not think that the Tempurpedic odor or smell is quite the same as some of those cheap memory foam mattress knock offs that you have to unroll like a carpet when it shows up and let it inflate.
Those China made foam mattresses are not the same as some of your more well known brands like Serta iComfort, Sealy TrueForm or Simmons Comforpedic. These are quality products that you spend a bit more for so you can have some peace of mind that it will last and provide a good nights sleep for a long time.
I would not be too concerned about the memory foam mattress smell as this will dissipate very shortly and you can even help it along buy basically breaking the mattress in with walking on it. You can accomplish two things at once in that regard.
If you are looking to save a bunch of money or just do not want to spend the big price Tempurpedic costs than just beware of the maker and make sure they have a good return policy and warranty in case it does not turn out to be what you thought it was.
In the end I think the advantages of a memory foam mattress outweighs the disadvantages and can be a big help in getting better est and therefore become healthier as a result. Remember to check for online promotions or sales before buying so that you can maybe save a few dollars on something you are going to buy anyway.