Does it do it with all your games? If it does then it could be one of two things; dirty optical lens on the disc drive - to fix this purchase a DVD/CD reader cleaner (looks like a normal CD with a small brush stuck to the underside.) The other is just dust affecting cooling. To do fix this purchase a can of compressed air and blow into the air vents to dislodge dust. Of the two I reckon your problem is the former rather than the latter.
was this right after an update, and did you try restarting your xbox?
I did update Max Payne 3, could that have been a source? I did restart it and did the hard rest I'm assuming by hitting guide and RT+Y. It did fix itself , although I'm not sure what "fixed" it(Played Max Payne for an hour or so after restarting it a few times)
For some reason it seems my system is actually cracking the inner ring on my games(I noticed a large one on my Skyrim disk) and just yesterday one formed after a four hour horde session I found a crack forming on my Gears disk, the games still run fine but i've been panic installing as many disks as I can.
I believe that the disc drive in your 360 is applying excess pressure to your discs. I don't know how to physically fix it but you'll either need to replace the drive by sending it to Microsoft for repairs or replacing it yourself. Sadly the alternative is to replace the entire console. I'm sorry I can't be of any real help.