Can a crown be placed on a central incisor that broke off at the gum line?

Depending on the condition of remaining tooth root it may, or may not be a good idea to invest more money into it by trying to save it. Restoring your tooth at this point would most likely involve: removal of broken post (yes it can be done), crown lengthening (a cosmetic challenge for front tooth), new post and crown. Extraction with a dental implant may be a better option both cosmetically and functionally (it would last longer).  

If the tooth broke off at the gum line, then it would be very heroic and unpredictable treatment placing a successful and long lasting crown on it.  Can the post be removed and a new one placed, possibly.  However retreatments are not as successful as first time treatments, and the tooth would most likely be weaker than the original post and crown that was placed.  Rather than "waste" time, money and effort on a treatment that will most likely not last, this is usually the "time to punt".....extract the root and place another type of restoration.Your four choices are:1) an implant and implant crown2) a fixed (non removable) bridge (capping the adjacent teeth which is attached to a replacement tooth)3) a removable partial denture or "flipper"4) do nothingChoices #1 and #2 are usually the best treatments.  Over the years fixed bridges have been done the most commonly, but this is being overtaken (by patients who can afford them) by implants.  If you are looking forward to dental insurance paying for implant treatment you will most likely be disappointed....sorry.  Dental insurance most often pays for "least costly alternative treatments" rather than "the best" or what the patient wants or dentist recommends.