There is the legend of Wan Hoo. This legend was first published in 1909 in Scientific American using the name Wang Tu but seems to have come from an earlier source. There are no Chinese records of the event from the time when it supposedly occurred. Although I suppose an event where a man blows himself up on a rocket chair is probably more likely to make it into popular legend than into history. With that disclaimer out of the way on to the story...

In his 1944 book Rockets: The Future of Travel beyond the Stratosphere (the book that would evolve through several editions into Rockets, Missiles, and Outer Space), Willy Ley tells a story:

Another such isolated instance of the application of rocket power is a story which may be legendary or it may be true-- there is no way of telling. It centers around the otherwise completely unknown person of a Chinese official whose name is given as Wan-Hoo.

This Wan-Hoo, the story goes, committed a rather spectacular suicide in or around ad 1500 by inventing and testing a rocket airplane. He took two large kites and connected them with a framework in the center of which a saddle was fastened. Forty-seven large powder rockets had been attached beneath the kites in strategic places and forty-seven coolies stood ready with flaming torches to ignite these rockets at a prearranged signal. When everything seemed ready, , the learned and daring Wan-Hoo seated himself in the saddle and finally signaled to the waiting coolies. They rushed at the machine, each one applying his torch to the rocket he was to ignite, and Wan-Hoo and his machine disappeared in a noisy cloud of black smoke.

source for the above quote Not a scholarly page but it provides the quote from the 1944 version that was modified slightly in the 1945 version of Willy Ley's book. I prefer this version.

Wan Hoo did eventually make it to the moon when a crater on the far side of the moon was named after him.

There's an amazing portion of Lucian's "True History" wherein the narrator's fleet gets swept up into the stratosphere:

About noon, when the island was no longer in sight, a whirlwind suddenly arose, spun the boat about, raised her into the air about three hundred furlongs and did not let her down into the sea again; but while she was hung up aloft a wind struck her sails and drove her ahead with bellying canvas. For seven days and seven nights we sailed the air, and on the eighth day we saw a great country in it, resembling an island, bright and round and shining with a great light.

That island being, of course, the moon, which is inhabited by a variety of colorful beasts. Highly recommend reading the story - it is one of the first examples of science fiction.

Source: True History by Lucian