I've been noticing this recently, it's amazing that such a basic issue is unresolved. Apparently overflow: scroll has been broken on android browsers since 2009[1], but was fixed as of Android 3.0. For me scrolling works fine in the native android browser, including overflow:scroll, but shockingly not in Android chrome.

[1] https://code.google.com/p/android/issues/detail?id=6864