Environment: Android
The Chip component does not wrap long text even when setting styles in textStyle prop and style prop:
<Chip textStyle={{ flexWrap: 'wrap' }} style={{ flexDirection: "row" }}>{message.text}aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa</Chip>

When using the following:
<View style={{ flexDirection: 'row'}}>
<Text style={{ flexWrap: 'wrap' }}>{message.text}aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa</Text>
</View>
Note: The message.text contains a new line character.

Chip should be a compact component which contains only the most important information. I think that multiline option shouldn't be supported (it's against MD guidelines).