Yes and no, So lets start with the yes, the analog or the thumb sticks, there are almost a dead on size of the Xbox 360 controller thumb sticks, 360 fit prefit and the are way cheep, here a link where you can buy multiple colors and also metal ones if you like. http://www.ebay.com/bhp/xbox-360-analog-sticks
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Yes and no, So lets start with the yes, the analog or the thumb sticks, there are almost a dead on size of the Xbox 360 controller thumb sticks, 360 fit prefit and they are way cheep, here is a link where you can buy multiple colors and also metal ones if you like. http://www.ebay.com/bhp/xbox-360-analog-sticks
Also here's a video to show you how to replace them. https://www.youtube.com/watch?v=FVtBPAifSmI
Good luck and have fun, love the Ouya
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=== Update (03/19/2016) ===
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You will need to use 9mm Xbox 360 thumbsticks to take up the gap on the Ouya controller, here's the link to the place that sells the products that you will need , Good luck. https://modsticks.com
Yes and no, So lets start with the yes, the analog or the thumb sticks, there are almost a dead on size of the Xbox 360 controller thumb sticks, 360 fit prefit and the are way cheep, here a link where you can buy multiple colors and also metal ones if you like. http://www.ebay.com/bhp/xbox-360-analog-sticks
Also here's a video to show you how to replace them. https://www.youtube.com/watch?v=FVtBPAifSmI
Good luck and have fun, love the Ouya