The Manitou Incline, near Manitou Springs, Colorado, was constructed as a funicular in 1907. It operated until 1990, when a rock slide washed out the rail bed. Since then it has been used for hiking, and has become a very popular test piece for endurance athletes. The Incline starts at 6600 feet elevation and gains 2000 feet in roughly a mile. The old railway ties form many steps along the route. In recent years work has been done to improve the tread and steps, and to make the Incline safer for hikers. competitor.com has a nice article on the Incline and some of the FKTs.
Official Incline times are simply from the first railroad tie to the last one. A Strava segment for the ascent is here: https://www.strava.com/segments/962740
Pro tri-athlete Mark Fretta appears to have the FKT for an ascent of the Incline, at 16m42s, set in 2006. There has been some controversy around this due to Fretta's sanction in 2012 by the US Anti Doping Agency, and whether his time was actually to the top of the Incline. Olympic speed skaters Ryan Bradford and Apolo Ohno also apparently ran the ascent in 17m41s and 17m52s, respectively, on the same day as Fretta, but again there is uncertainty about where exactly these athletes stopped their watches. Locals do not consider these times valid, so we don't Fretta's time as the FKT.
We have FKTs for the Ascent, the "Inclinathon", which is 13 round-trip laps of the Incline, adding up to about a marathon with an incredible 26,000 feet of vertical gain, for the most laps of the Incline in 24 hours, and for the most ascents in one year.
Lots of locals to not believe Fretta's claim for this FKT. Seems like it least deserves an asterisk. See this story for more details.
Oops. Guess this site doesn't like links. Just Google: "Joe Gray Breaks Matt Carpenter's Manitou Incline FKT"