I agree with the other advice that you should counter the offer. Yes, it's possible, as the others suggest, that maybe the market is trying to tell you that you're overpriced. But maybe you're not overpriced. Maybe the person making the offer was just testing the waters. I often post here that, when making an offer, a buyer shouldn't worry about "insulting" the seller. And I stand by that. On the other hand, sellers shouldn't be "insulted" by a low offer. At the very least, it is an offer. Unlike others who may have viewed your home, this person is saying, "Yes, I could see myself living there. If we can agree on a price, I'm willing to buy." And that's a good thing.To use an analogy, you've got a fish on the line. Can you reel him in?
Even the somewhat Realtor-hostile response from Beeja (saying to discount the advice here and Google for an answer) provided a link to RealtyTrac. The advice there on RealtyTrac says in part:
In most cases, the first offer you receive will be at least slightly less than your asking price. This is to be expected and does not necessarily mean that you need to take the offer as is or halt all further discussions. A common trap FSBO sellers fall into is the desire to stop all negotiations with a potential buyer simply because they are insulted by a low offer. Keep in mind that a buyerâ€™s initial offer rarely represents the highest price they are willing to pay. Rather than throw away a possible sale, you should take the opportunity to draw up a counteroffer.
Meanwhile, double-check the value of your property. If you asked a Realtor for comps initially, ask for another CMA. If you used some other method, at least revisit that. Prices and values do change, even if you started off at a reasonable number.
Hope that helps.