Dec 26th, 1783. Louis-Sébastien Lenormand was the man who did the deed. From Wikipedia:

After making a jump from a tree with the help of two modified umbrellas Lenormand refined his contraption and on December 26, 1783 jumped from the tower of the Montpellier observatory in front of a crowd that included Joseph Montgolfier, using a 14 foot parachute with a rigid wooden frame. His intended use for the parachute was to help entrapped occupants of a burning building to escape unharmed. Lenormand was succeeded by André-Jacques Garnerin who made the first jump from high altitude with the help of a non-rigid parachute.

BASE jump? It stands for someone who jumps from Bridge, Antenna, Structure (building), Earth.