In nature, fearless mice are known as "food."
Edit: Thsi sounded familiar. Something similar has been done before:
http://www.nih.gov/news/radio/dec2005/12162005mice.htm
Researchers have found that by knocking out a gene in the brain, they can create a mouse that is not bothered by situations that would ordinarily trigger instinctive or learned fear responses — hence a living, breathing "Mighty Mouse". According to a study funded by the National Institutes of Health, a gene in the mouse brain encoding a protein called "stathmin" appears to be critical in forming fear memories.