In some areas of Illinois, it is becoming more common to sell a decedent's home without probate. It is not always a viable or recommended option, but it may be possible with the approval of the title company and potential a bond in lieu of probate.
If the home is the only asset your parents had, and especially if it has been more than 2 years since your parents passing, I suggest you contact a local lawyer that does both real estate and probate law to go over the pros and cons with you of probating or not probating your parents estate.
Only your parents have the right to sell their house, and if they have both passed, then a court (in this case a Probate court) needs to give someone else the authority to act for them.
In short, if the home was in the name of your parents alone, then the house MUST be probated to be sold. Please do not assume that probate will be time consuming or expensive however, as if done correctly it can be a pretty painless process. I strongly urge you to contact an attorney licensed in the state your parents lived in to insure you petition properly to insure the case proceeds as smoothly as possible.
Your answer depends on whether your parents added you to the deed prior to their passing. If they did add your name, then there is a good chance you can avoid the probate process since you are the surviving owner of their house. As part of the sales process, you would supply the title company, among other things, with your parents' death certificates. The title company can get access to the recorded deed that added you as a grantee. You would then be able to sell the house without going to probate.
If your parents did not add your name to the deed for the house prior to their passing, then you will have to hire an attorney to start the probate process. It can be a relatively straight forward process where your attorney would be able to walk you through the necessary steps.
This would be better reviewed in an office consultation or telephone call. Probate can be avoided in certain circumstances by working through a title company. Depending on the timing, there may be an additional title premium. If there are concerns, such as bills for which the estate is responsible, unknown claims, uncertainty concerning heirs, missing heirs/legatees, or similar matters, probate may be best to assure that the estate is fully settled. I would be pleased to discuss this with you.