What do you think was the mostly unpredictable and random discovery in chemistry?
By my opinion it was synthesis of C6(OH)6 (hexa hydroxy benzene) by passing of CO above melted potassium:
6K + 6CO = C6(OK)6
C6(OK)6 + 6H+= C6(OH)6 + 6K+
Unbelivable, isn't it?
 

As a synthetic organic chemist, I would go with Perkin's inadvertent discovery of mauveine (c. 1856) that ultimately led to the chemical dye industry.  He was attempting to make the natural product quinine (found in tonic water, by the way) by simply heating 2 equivalents of N-allyltoluidine in the presence of oxygen.  Today, this would be a laughable experiment since there is no chance that the sponataneous formation of quinine would occur.  Perkin found that the reaction produced a black solid.  At this point, any modern day chemist would probably give up, but Perkin attempted to extract this tar with a variety of solvents and found that when he extracted with alcohol he obtained a brilliant purple solution that was a potent dye for fabrics.

Perkin made a lot of money off of that discovery.

A very cool polymer indeed. It looks just like metal.

I like the discovery of cold stretching polymers myself.  The first thing the DuPont scientists did with their gloppy pile of nylon was see how far it could stretch down a long hallway.

I'm also a fan of Archimedes and his discovery of buoyancy.  Sure, it's not chemistry, but the story has a great mental image.

indigo was formed as a result of pyruvic acid phenylhydrazone rearrangement under acidic conditions.

You mean a Fisher indole synthesis?!