Like many banks, Bank of America will check to see if you have any negative history with Chexsystems. However, having a negative report in Chexsystems does not always mean Bank of America will automatically decline you.
After searching on the Internet, there were several people who were able to get an account with Bank of America, even if they had a negative report with Chexsystems.

Each local Bank of America branch and banking center does have rules and guidelines that it must go by when making decisions about whether or not to open an account for someone. There is also the option of opening an account online. The guidelines that all local institutions must follow change often.
Since 2000, Bank of America has looked at the reason why someone has been listed in Chexsystems before deciding to decline them an account. So, just having a report at all may not keep you from getting an account with Bank of America. It depends on two main factors – how long it has been since the negative reported activity occurred, and how severe that negative reported activity was.

For example, say you didn’t realize you hadn’t closed an account; it accrued bank fees and was automatically closed. You later found out you owed this money to the bank, and paid it. This all took place three years ago. Since it is less than five years, it is still in Chexsystems. It is not fraudulent, and you did pay the money owed. Bank of America would be more likely to give you an account in this situation.

Bank of America is less likely to open an account for you if your account includes fraudulent activity or shows that you still owe large amounts of money, or if the negative report was very recent.

There are many reports from people in Internet forum boards who had been reported to Chexsystems and were able to get Bank of America checking accounts by opening them online, after they had been turned down by their local in-person walk-in Bank of America branch. If you already know you have negative information about you in Chexsystems and you want a Bank of America account, you may want to try applying online for an account first. Even though many report it is easier to get an online account, you would avoid the possibility of getting declined by a local branch and then having an online Bank of America see the recent decline.
Of course, if you didn’t know you were listed in Chexsystems, and went to a branch and were declined, you can always try applying for an account online.