There are two options here and they both relate to how the chip is constructed. The whole chip is a div container. When you add media to that chip then inside that container a media div is added. The same is true for the label. So if you have media and a label you get a structure like this:
When you add an icon to the media, it’s inside the chip-media div so changing the icon’s positioning only changes it inside that div and not relative to the label.
So, your two options are:
Use a stylesheet to change the positioning of the chip-label div
Don’t add the text to the chip itself (which removes the chip-label div) but add a Label component to the chip media in addition to the icon which you can then position relative to the icon within the chip-media div:
You probably want to adjust the padding values on the chip (adjusting the actual width will have negative consequences for the alignment of the components inside).
Since it grows in width, probably just padding-right: 5px, and padding-left: 5px will be sufficient.