(edited to adjust diagram per jsotola)
As I'm working from home I've missed a handful of times someone dropped off a package due to the doorbell being upstairs while I am downstairs. I'd like to add a second doorbell chime (single button still on the front door). I have access to the transformer in the utility room (I actually want to put the doorbell on the exact opposite wall), I just don't know if I can wire a second chime without doing a bunch of work pulling doorbell wire. Here is how I understand (note, I could be wrong, all the wiring is behind a wall) the current setup to be
I'm just not sure which of the two options below is the correct way to wire them. I believe I can manage the series wiring if that is the correct way to wire a second chime, but if not and the correct way is parallel that's out of my motivation range as I would need to snake wires through both exterior and interior walls.