You don't want to clean a copper chiller so it is shiny - if you remove the dull color (stable oxide), the metal is more likely to react and form the toxic blue-green oxide (verdigris).
Copper is relatively inert to both wort and beer. With regular use, it
will build up a stable oxide layer (dull copper color) that will
protect it from any further interaction with the wort. Only minimal
cleaning to remove surface grime, hop bits and wort protein is
necessary. There is no need to clean copper shiny-bright after every
use or before contact with your wort. It is better if the copper is
allowed to form a dull copper finish with use.
However, you need to be aware that copper can develop a toxic
blue-green oxide called verdigris. Verdigris includes several chemical
compounds — cupric acetate, copper sulfate, cupric chloride, etc. —
and these blue-green compounds should not be allowed to contact your
beer or any other food item because they are readily soluble in weakly
acidic solutions (like beer), and can lead to copper poisoning (i.e.,
nausea, vomiting). To clean heavy oxidation (black) and verdigris, use
vinegar or oxalic acid-based cleansers like Revereware Copper and
Stainless Steel cleanser.
For regular cleaning of copper and brass, unscented dish detergent or
sodium percarbonate-based cleaners are preferred. Cleaning and
sanitizing copper wort chillers with bleach solutions is not
recommended. Oxidizers like bleach and hydrogen peroxide quickly cause
copper and brass to blacken; these oxides do not protect the surface
from further corrosion, and are quickly dissolved by the acidic wort.
Copper and other trace metals are beneficial nutrients for yeast, but
the amounts that are dissolved from non-passive oxides can be
detrimental to the batch.
Copper counterflow wort chillers should not be stored full of
sanitizer or water. Any biological deposits can lead to corrosion in
both water or sanitizer. Copper should be rinsed thoroughly with clean
water and allowed to drain before storage.