I have read on other sites that this is a collection agency seeing if they have the correct phone number. They disguise themselves as a chimney cleaning service company, they ask for your name and then hang up. When you try to call back the number 860-346-6176 - you get an "out of service" recording. I don't have any outstanding bills so I'm not so sure it's a collection agency.
To all posting here, especially those above who mention that the number is not working or comes back to a chimney cleaning service. You should take note that the telephone number is more than likely "SPOOFED". Meaning that there are computer programs that allow a caller to have ANY telephone number show up in your caller ID. This is usually the case and you do NOT see the real number. The scammers and marketing nuts use the internet (like Magic Jack) to make calls for about nothing and then program whatever telephone number to show up on your caller ID.