Hi @j_j,
At this time, it is not possible to reposition the live chat widget.
I certainly see value in being able to do so, however. I recommend upvoting and commenting on this HubSpot Community Idea to help it become a reality. This information is sent directly to our Product team and helps prioritize feature requests that have the greatest impact on our customers. I’ve already upvoted the idea and will also do my part and pass your feedback along through internal channels.