Translation:It is not near.
Yeah, it even gives that as a translation when scrolling over the characters, but marks it as wrong.
Agreed I was taught that ちかくis nearby but keep in mind that near and nearby have essentially the same meaning. You need the くnetween the adjective and ない though. So in that sense nearby would be ちかくくない。
Traditionally -くありません is the most correct way to negate い-adjectives, but I think that -くないです is used much more common nowadays.
ない translates to "not". ありません is the negative form of あります meaning it is more formal. ない is more common but good to know, especially for words like these that sound wrong using ありません.