What connotation does a unicorn have?
It has a very positive connotation. It is described as a rare and beautiful animal. It also has great magical powers.
In "Harry Potter and the Philosopher's Stone" by J. K. Rowling it is said that when a man drinks blood of unicorn he will survive no matter what happened to him earlier, but on the other hand killing (or even hurting) unicorn is described as a great crime.