BETA PHOTO: Blurry, but shows the route very well. You can't m...
In spite of its name, this is a completely reasonable climb to introduce kids or the timid to climbing. Any competent climber can solo this route without much of a problem. It can be used to get down from adjacent climbs or to set top ropes on them, and it's also a good location for mock leading.
Climb the chimney right of Horseman and just left of Laurel. There are rappel bolts on top of Laurel.
Major tree-fall removed a huge tree from this route in 2010.
I think Dirty Chimney offers about the best 50 feet of readily accessible 5.0-5.1 climbing I've seen in the Northeast US. At most climbing areas, the easy routes are slabs. Leave it to the Gunks to offer one with interesting holds. It's fun to look for the "hidden" holds that make it only 5.0-5.1 (and avoid using actual chimney techniques). Yes there is some dirt around (more if you go beyond the ledge on top of Laurel, all the way to the top of the gully, which I don't recommend) but most of the footholds and handholds are usually fairly clean (? except after a big rainstorm ?).
So if you just don't like climbing in enclosed spaces - or easy climbs - or short climbs - then of course don't do it (but then please don't whine about it).
If you are looking for interesting 5.0-5.1, perhaps intrigued by climbing in a 3-dimensional space, well here it is.
I still like it two years later (after not climbing it at all in the 2012 season because of a warning sign).
I guess that a few feet below the top of the lower "chimney" section, most people exit to the right to the bolt anchors for Laurel. It's a little harder to continue directly those last few feet to the top of the lower section.
The upper section is indeed dirtier -- and has a tricky exit move at the top of the whole climb -- might be 5.2