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It really just depends on what is important to the landlord. I rented my current apartment with multiple charge offs. This was ten years ago. I love my apartment and apartment community and the next time I move, I want it to be into a home of my own. So, I landed well even with troubled credit. In any event, my application was approved because I had never screwed a landlord and always paid my rent. I wasn't required to pay an additional deposit. When putting in my application, I explained my credit situation and that I was working on it. Having a high-paying job helped. So, I think just explain your situation and show that you can afford the apartment and that you are working on the charge off. But don't let them run your credit and find out on their own. Tell them first, and do so in person if you can, get them to like you. This is how I handled it. Get ahead of it as you apply. Oh, and ask your current landlord if they would write a reference and always send it with your application. Good luck!
Have you pulled your credit reports from all three bureaus to see what they show? It's possible that the default was reported to one or two bureaus instead of all three. In that case, you might check with landlords to see which report they pull (if any). You should probably also get your credit scores from all three so you'll have a complete picture of your credit history.