Hello, Steve
As a real estate broker I have gone through many home inspections with certified home inspectors. And as a homeowner, I have had home/s I have sold inspected for the buyers.
The quality and character of a home inspector varies, as does a building contractor or garage repairman. There are well-qualified, and poorly qualified inspectors. There are reputable ones and irreputable ones. Most serve a very good purpose - they have more knowledge than most people buying homes, and inspect things most buyers wouldn't even think to check. They are far less expensive than paying different contractors (HVAC, plumbers, electricians, brick & mortar specialists, etc.) to inspect all the various features of your new home - especially since your home is probably the most expensive investment you will ever make. They can bring attention to possible areas of concern (remember they have general knowledge) - take those items in question and then go to the specialist.
Now to your specific situation - your home inspector may or may not be right, but the chimney is not a place to try to become your own specialist on the cuff. Have the chimney inspected by a qualified fireplace/chimney contractor. At the very least, your chimney may need to be cleaned (build-up of creosote from wood that may have been burned can cause a fire in the chimney - a far more costly possibility.
You did very well to have a home inspection. Whether the home inspector is right or wrong, paying a contractor to have that verified will be money well spent. Better to spend a little than risk you, your family and your home.
Best wishes and enjoy your new home! Karen
PS - Happy Veterans Day to all our Veterans! November 11, 2003