If you're having trouble signing into your Xbox Live account today, you're not alone. According to the Xbox Live Service Status page, Microsoft is currently experiencing issues with the Xbox Live Core Services, knocking out the ability to sign in. From Microsoft:
Hey Xbox members, are you having issues signing in to Xbox Live? We are aware of this and are working hard to get it resolved ASAP! Thank you for being patient in the meantime. We'll post another update when more information becomes available.
The outage looks to be affecting signing into Xbox Live across the Xbox One, as well as apps and services on other platforms. Microsoft is aware of the issue, and we should see it resolved relatively soon. For now, you can follow along with the Xbox Live Status page for updates.
Update: It looks like everything is back to normal, folks. Happy gaming!
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Source: Xbox Live Service Status