Wouldn't you then continue to see more prolific mutations, like the blue ( or black) has become?
The basic red junglefowl coloration (chicken calculator, all genes marked +) is the original form. ALL the other genes we know about are mutations.
http://kippenjungle.nl/chickencalculator.html
When people start examining the exact mechanism, they find that mutations are commonly caused by DNA that copies a little bit wrong when forming new cells: something gets missed, or duplicated, or transposed, or a similar error. There is also at least one (blue egg gene) that is considered to be from retrovirus DNA getting added to the chicken DNA (once it was in the DNA of a chicken, it could be inherited like any other chicken DNA: remarkably like genetic engineering, but in this case it happened naturally.) Some of those mutations have no effect, some cause a problem that kills the chicken, and some cause effects that people notice and want to preserve.
Mutations are definitely continuing to occur.
The "chocolate" gene is a fairly recent one, while the one for short legs (Dorkings, Japanese bantams) has been around for thousands of years. Any mutation that people notice and deliberately breed, will tend to stick around (crested heads, silkie feathers, feathered feet) and may become common (black, silver, dominant white, brown vs. white eggs). But a mutation that kills the chicken, or that people just do not find very interesting, will tend not to be common (ear tufts on Araucanas: one copy of the gene will cause ear tufts, but two copies will kill the chick, and most people do not like ear tufts enough to put up with that. So the vast majority of chicken breeds and crossbreeds do NOT have ear tufts.)
I suppose the question would be, is there some sort of limit on genetics, at least for colors?
For instance, what about hot pink? Is there a scientific reason why their would never be a mutation that would cause a chicken to have hot pink feathers, that could then be reproduced.
There are some limits, but I do not know exactly what they are.
It seems that many mutations are actually making something not work quite right. Examples would be blue (causes black pigment to not form properly) and silver (blocks the formation of red pigment) and barring (intermittently blocks the pigment formation, creating unpigmented white "bars.") But some other mutations cause pigment to spread further than it otherwise would (example: Extended Black). And some mutations cause a substance to be deposited in the eggshell (blue eggs) or the skin & fat (yellow skin vs. white skin), when it otherwise would not be.
Chickens and mammals seem to naturally form red pigment and black pigment, so most colors that we see are variations of those plus white. "Blue" in birds such as bluebirds and peacocks is caused by a structural change in the feathers so it reflects light differently, not an actual blue pigment. (Similar mechanism to what makes the sky appear blue.) I have seen at least one chicken that appeared sort-of pink (I think it had white and red in a way that looked pink from a distance), and it's common for people to call some eggs "pink." I do not know whether a chicken or egg could appear actual "hot pink" instead of a brownish-pink.
If you want to go into more detail, I see this as a possible starting point:
"In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism,"
source:
https://en.wikipedia.org/wiki/Mutation
Personally, I haven't cared enough to go much past what I put in this response.