Letter from the Land Registry
In the event you should get a letter from the land registry the first reaction should be not to panic because it may not be that bad although without a doubt there is going to be some concern and you will need to do some research yourself.
The first action should be to look at your property deeds and to see what they say do they mention ecclesiastical dues or liability to repair or some similar kind of statement within them and that point it is likely that the notice is genuine.
No matter what your deeds say I believe any property owner should immediately object and use the appropriate form from the land Registry probably UN4. This will give some breathing space.
It is possible that you have chancel repair insurance in which case you check on it's terms but it will probably only protect you if the PCC came asking for money which may not be for many years. It is unlikely to mitigate the negative consequences of the registration to the title of your property.
Ascertain the Liability
You may be liable but chancel repair is very complicated and it is possible that there are other liabilities in the parish that the PCC missed and other owners are jointly liable with you and then I believe speaking to a specialist solicitor to see if you could register on other properties is a way forward.
Or you may discover the PCC make a mistake and registered your property incorrectly in which case you can have the notice removed.
Previous owners of the land
Check in the conveyance documents of the land since there are a number of cases when previous owners of the land indemnify all future owners this may be mentioned explicitly or it may say something like 'land sold without ecclesiastical dues'. This could be great if it is a large organisation or the estate is still around and wealthy or completely valueless if the estate has ceased to exist. This might also explain why the PCC is registering since they, like you, will not know the state of any indemnification. If this is true then as a matter of urgency discover the terms of the indemnity and contact the relevant estate.
Paying the PCC off
If the liability on your property is apportioned with a small amount of liability then compounding or paying the PCC off is a real possibility and this could well be a relatively small sum. If you think this is a way forward then the first port of call is the local Diocesan Board of Finance and offer to compound the liability under the 1932 Chancel repairs act . The only chancel which is known to have been compounded in the recent past was Aston Cantlow and the compounded value of that chancel was £36,500 for an entire chancel.
(minor update 7th October)