In the very first episode of Life is Strange, we see Chloe confronting Nathan in the school's bathroom. We later find out that Nathan has been dealing drugs to other students -- and at one point, even drugged Chloe (something we will probably witness in Life is Strange: Before the Storm). Because of such actions, Chloe decided to use that information to extort money from Nathan through blackmail.
Chloe needed the money not only to pay Frank back, who lent her a pretty penny (around $3,000 actually) that was most likely needed to fix her truck, but also to have a little extra for herself and Rachel when the two planned to escape from Arcadia Bay. But ever since Rachel disappeared, Chloe really needed the money to pay Frank back.
In a way, this would tie in with Chloe attending Blackwell Academy since that is where she first met Nathan and found out who he is and what his deal is, and how their first "adventure" began.