"alath" wrote in message
Since there are no obvious problems up above, I am wondering if there
may be moisture coming from inside the chimney somehow? It is
suspicous to me that we only started having this problem when the
weather got cold and we were running the furnace. Of course that could
be a coincidence, if the previous owner did a patch job that held for
2 years, and the underlying problem is only now starting to reveal
itself.

Does anyone have any suggestions to help me diagnose and repair this
problem?

To say for sure, you'd need a reputable chmney inspector. It may be from
condensation. One of the products of combustion of natural gas is water.
With the cold weather, it will condense in the chimney and drip back down.
There may be some blockage from an animal next in there too making it worse.
Liner may have cracked allowing it to seep through.