Can I sue a fast food chain that is located next to my property for excessive noise?

First, if they are making noise late at night, they may be violating municipal noise ordinances; try reporting them to the authorities for that. (Contact the police; they are often involved in enforcing these ordinances and even if they don't in your municipality, they can direct you to the correct department.) If they or their patrons are in violation, they can be ticketed, and ticketed repeatedly (i.e. forced to pay fines), until they stop. Similarly, if they are violating littering or health ordinances (e.g. by the garbage), they can be ticketed for those things, too. So looking into the rules/ordinances for these things (the municipal clerk's office can help you find those ordinances) is a very good way to start,  since if they are in violation, the city can enforce the rules against them without you having to pay for your own attorney or lawsuit.
If they are not violation and/or being ticketed, etc. does not stop the behavior, you can try suing based on "nuisance"--on this being inappropriate behavior for your neighborhood (e.g. if the neighborhood is partially or mostly residential, having noise later at night than it should be, where children and families sleep). But be warned that nuisance suits are very difficult if the conduct/use (e.g. having a fast food restaurant) is permitted--e.g. it properly zoned and permitted. The presumption is that otherwise legal activities may be conducted; overcoming that presumption and showing that the use is a "nuisance" despite being permitted is not easy. If you do win, you can get monetary compensation and/or a court order that they change what they are doing, but you could spend a lot on the lawsuit with no guaranty of winning: that's why trying to get them cited for ordinance violations is the better thing to start with.