The answer is the first one: "to take advantage of". This is the more common meaning, and also the more flexible meaning, with common collocations being:
... as well as several well-known 成语, like:
趁热吃 is very idiomatic, and commonly heard in Chinese households.
It can also be used in clauses, often in the durative 趁着, as found in e.g. a casual search of novels on Google Books:
"To have a lot of" is a marginal meaning in modern standard Mandarin, fossilised in the expression 趁钱 to be rich in wealth, to be wealthy, which also has a homophonous variant 称钱. In other varieties of Chinese, e.g. Min varieties, this expression means to earn money; this is possibly how the meaning was extended, although that is currently just speculation.