My Mother and Father bought a condo in 1996 and put my name along with theirs on the title. They now have sold it. Am I obliged to capital gains on the property?

This is some poor tax planning ... you should have quit claimed the property BEFORE it sold.  So whose names are on the closing statement ?   Did they issue you or your parents a 1099-S ? 

Thanks for the help. The closing won't happen for another three weeks. My share will also be put towards the new home which will be my permanent residence. Does that matter? 

My name is on all of the docs

Ok ... seek out a real estate attorney or talk to the closing company ... YOUR name must come off the deed before you sell or you may be responsible for taxes on 1/3 of the profits.  What your parents do with the profits of their home sale is immaterial to any of you. 

Thanks for the advice, it's appreciated 🙂  

You should see a tax professional immediately, and then you probably need to see the attorneys who are handling the closing.  It is very likely that you will owe capital gains tax on 1/3 of the gain if the house is sold in its present condition. However, this is not 100% certain because it depends on how your parents gave you the property in the first place.  It is also very likely that you can give your share of the house back to your parents before they sell it, and avoid paying any tax. The gift would probably have to be reported, but no gift tax will be owed unless your lifetime total of all gifts and your estate is more than $11 million.

Then, once you have extracted yourself from this situation, see an estate planner, usually a law firm with financial experts on board, before you make any future moves.  Depending on exactly what you are trying to accomplish (avoiding probate or protecting the house as an asset in case of long-term medical costs) there are ways to do it that do not put you at extra tax risk.