The easy answer is to hire a mason to look at it for you. I guess the best thing would be to get that chunk, or talk to the person who found it, and relay that info to your mason. Did you see the chunk? Can you determine whether it is a chip or is the flue broken through? Maybe it's a chip and they will shrug it off. But I'd think about getting a pro's opinion, especially if there are other potential brittle areas. Did you have a fire? Did you hear a whooshing sound once, or find ash and junk on the roof or ground? There are little fires in chimneys all the time, but what damages them is the intense ones.
How handy are you, and will you sleep at night with your own repairs? This might sound like a funny question, but the time and trouble in making your own repair, coupled with the subsequent worry, sometimes isn't really a savings in the long run. Having said that......
I have read about a couple methods for repairing stuff that is out of reach. One is to pull a burlap bag tightly filled with straw (or moss, or similar material) and topped with mortar up through, which would fill the voids on the way. Kinda like a Q-tip in reverse/w3tcompact/icons/tongue.gif! That's an old fashioned method of sealing cracks I have read about. I've also seen ads for flue installation where they insert an inflatable tube down the chimney and pour mortar around it - I don't think you need that.
I am running a wood stove in an old (35 years) concrete block chimney lined with 8x8 tile, and the they seemed to "wander around" when they built the chimney. It's as if they cut holes in the house and aimed at them with the chimney. You can see the ends of the tile a bit when you look down or up the flue, and there is a noticeable curve in it. Our flue also ends where the pipe entrance is, about 48" off the floor. The builders mortared spikes into the block, and set the whole tile liner on that - a scary and cheap way to save a couple pieces of tile and avoid cutting one. We had a few cracks, even a large piece broken out, but they were easy to reach, and I patched them up and smoothed the entrance with mortar. I mortared over the nails to seal the flue at the bottom, too, something that makes me wonder if the nails will now corrode, but I've seen metal in mortar before and it seems to be fine. We used to wonder if we would wake up to the sound of all the flue suddenly sliding the last 4 feet to the cellar floor! We've got a couple seasons on the wood stove now, and it seems to be operating well.
Might be the best thing to do is call a mason. I'd like to know how you make out.