You have nothing to worry about. These energy efficient light bulbs, or CFLs as they are also often called, are completely safe.
The chemical you are referring to is mercury. Its true that mercury is a dangerous chemical, but the amount of mercury in a CFL is only 4 milligrams. This can be compared to the 500 milligrams that are inside every old-style thermometer that you put in either of your orifice. Here's another example to put things into perspective: a can of tuna, sadly, contains as much mercury as a CFL.
That said, its important that you don't buy the cheapest brand and that you recycle your broken CFLs.
Energy Star says this (pdf) about CFLs:
"CFLs contain a very small amount of mercury sealed within the glass tubing – an average of 4 milligrams (mg). By comparison, older thermometers contain about 500 milligrams of mercury – an amount equal to the mercury in 125 CFLs. Mercury is an essential part of CFLs; it allows the bulb to be an efficient light source. No mercury is released when the bulbs are intact (not broken) or in use.
Most makers of light bulbs have reduced mercury in their fluorescent lighting products. Thanks to technology advances and a commitment from members of the National Electrical Manufacturers Association, the average mercury content in CFLs has dropped at least 20 percent or more in the past several years. Some manufacturers have even made further reductions, dropping mercury content to 1 mg per light bulb."
So in conclusion: CFLs are safe. Switching from traditional light bulbs to CFLs (or LEDs) is an effective way to save money and electricity.
In my country public transportation is good and clean. I often travel in public buses. But we are four friends who are working in same building so we are sharing car. I think that this is also good step for saving environment.