Amazon offers the the Microsoft Xbox One Console bundled with downloads of Assassin's Creed Unity and Assassin's Creed IV: Black Flag for Xbox One and $50 Amazon Credit for $349 with free shipping. (Microsoft Store charges the same with their own $50 gift card.) Assuming you'll use the gift card, that's the lowest total price we could find by $51 (outside of the mentions below), although we saw it for $19 less three days ago, since expired. It features a wireless controller, 500GB hard drive, a chat headset, and functions as a Blu-ray player.
A close price: Best Buy has it with a $50 Best Buy Gift Card for $349.99 with free shipping, while Newegg offers the same Unity Bundle with an Xbox Live 12-Month Membership and a $20 Newegg Gift Card for the same price.
Of note, Amazon orders placed via 2-day shipping today will arrive in time for Christmas. (This option is free for Prime members but an extra $14.48 for everyone else.) Microsoft Stores orders will not arrive in time for Christmas.