I see this usage frequently on various SE sites:
I've an [object]
This usage of "I've" seems very strange [edit: archaic or poetic] to me as a native speaker of US English. I'm accustomed to only creating contractions of "have" where "have" is an auxilliary verb, e.g.
In informal US English, you will often even see the redundant usage
I've got an [object]
Although this could also be parsed in a non-redundant way, as "I have [obtained]."
I don't see the first usage much in contemporary British English, either. It seems to be limited to non-native English speakers.
Is the first usage being taught, or is it an example of overgeneralization? Is it strictly wrong, or is it just unusual? [edit: Given the examples in some of the answers, perhaps it's coming back into vogue. I still feel like I should be speaking in a British accent and wearing a monocle when I say it.]