If it were my house? I would probably do it myself because I have a very easy access to the top of my chimney and I feel comfortable working from the roof or ladder.
A few days ago I was talking to a friend of mine who owns a 3 story / 3 units building and he received a chimney liner (approximately 40 feet) installation quote for $3500.00 (from some heating contractor). It’s a straight chimney, there are no offsets, and the installation is reasonably simple. Probably 2-3 hours max time including appliances flue connection and a new chimney cap installation.
Total material cost close to $600.00: stainless steel liner (no insulation needed since the chimney runs inside the house), new chimney cap, a few clamps and a “Y” for the furnace / water heater hook-up. With that information he started calling a few other contractors and finally got a quote for $450.00 labor only.
Each situation is slightly different and in some cases there might be significantly more labor involved, e.g. with corbelled (angled) chimneys, or exterior chimneys in cold climates where an insulated liner would be recommended. The liner would probably double the material cost and its installation requires more labor / depending on the chimney configuration it could be more difficult.
There is also a subject of connecting the liner to your appliances, in many cases the chimney wall opening where the furnace and / or water heater’s vent connector penetrate has to be enlarged for all the connections to be performed correctly.
So, I would definitely wait for that second opinion and maybe even get a couple more from your local heating contractors. The price ($2100.00) seems high but, as I have mentioned above, there might be additional labor / time consuming processes involved and it’s difficult for me to judge.
If you call for more estimates, make sure to ask contractors for the same thing: flexible (preferably stainless steel) liner, insulation (if exterior / exposed chimney and cold winters), new cap. Also, make sure they calculate diameter correctly based on your appliance(‘s) BTU ratings and a few other important parameters.
Let me know if you have more questions, just click “comment” under my answer (on my website