Finding design in nature is extremely difficult. First it would require that you have an actually designed life form to compare it with. But that aside I take exception to your suggestion that chemistry is simply "random". Actually it's not quite like that.
Yes, there is a component of randomness in any given reaction: the atoms and molecules need to literally bump into each other in the right orientation and with the right speed to react but that being said chemistry has nice rules to govern how and why it WILL react. The bonds that make up living things are EXACTLY THE SAME AS BONDS MAKING UP NON-LIVING THINGS. Life utilizes ONLY standard normal chemicals found in non-living systems. There is precious little that divides us from the non-living.
Even early "life" may have been little more than RNA molecules stuck to the surface of a rock and acting as a template to coordinate with and cause the reaction of other molecules leading to a crude form of "self-replication". But at the end of the day there are definitely RULES. So it is not purely random.
The reason we find parts of proteins and amino acids in meteorites is because this chemistry is NOT exotic. It is still basic chemistry.