You have a rosemary green thumb! I've rooted rosemary by bending a branch down and placing a U shaped piece of wire on the branch to keep it in contact with the soil, but that is outdoors. Your rosemary must be very happy to have rooted a branch indoors.
Keep the new plant. After you have a full compliment of rosemary, you can start sharing.

leira, just so you know: you've successfully achieved a type of propagation called 'layering'.

Don't do too much tugging on the offspring. When you're ready to pot it up, separate it with sharp instruments so that your cutting the roots, not tearing or smashing.\

Congratulations!

Rhizo brought up a good point, how to separate the baby from the mother! When I find that the new plant has enough roots (which is a matter of judging if there is a lot of resistance when given a gentle lift, and if the baby has been around for a while) I cut the stem leading to the mother plant, take a trowel and lift the baby with roots and soil ball, and transplant.

Another plant which can self-layer is thyme. It's wonderful when plants do that without any intervention by you!

I suggest you leave the baby attached to its mother for a while longer, and separate them in spring when they're more likely to be in 'growing' mode. And yes, treat those baby roots with great tenderness when you do it.

Yup, rhizo, I've done layering before, both on purpose and sometimes fortuitously, like this.

Daisy, I'd intended to help my common thyme to propagate itself last Summer, but I never did get around to it. I blame being extremely pregnant, and then caring for a small baby...but maybe next year, unless the thyme, too, has decided to take matters into its own hands.

Maybe I'll give it a shot with the lavender, too...layering for everyone!

My rosemary definitely needs a re-potting, as it got awfully big while it was outside over the Summer (you may all recall that I asked what to do with the extra roots that were poking out the bottom when I dug up the pot and brought it inside -- I clipped them off and left the rest of the plant as-is).

My plan is to re-pot the mother plant and separate out the baby when it's time to send them back outdoors again in the Spring. I'll probably harden them off in their current pot first, though. After this year, I'll need to seriously ask myself whether I want a potted rosemary that's quite that big, and I may need to change my "re-pot it in the Spring and let it keep growing" habits. But hey, I'll have a nice small rosemary to start over with, right? Plus the smaller pots vacated by its mother to keep it in. :-)

Congratulations on your new plant!

I just cut off two inches off the top of my rosemary plant dipped the end in rooting hormone and stuck in a pot. Everyone of the clippings have roots. I love rosemary. The mama outside I bought small in the spring. When it got to big for the pot I put it in the flower bed. I didnt realize it would become this huge bush. And evergreen.

I've successfully propagated rosemary from cuttings in the past, using rooting hormone and a plastic dome to keep the humidity in. I was actually expecting to do that sometime this Winter (and I guess I still might), but the mother plant beat me to it.

I also saw the other day that another branch is nearly brushing the potting soil as well, so who knows? Maybe it will happen again. I may pin this branch down, but I'm sort of curious to see what will happen if I leave it to its own devices. This mama rosemary sure does want a family!

This mother plant was somewhat small when I got it a couple of years ago, but I can't for the life of me remember where I got it. Probably from an herb sale at a local greenhouse (one that's been operating since the 1700s...wow).

Sadly, most rosemary varieties will never survive year-round outdoors in my zone, so in it comes for the worst of the Winter. The best lesson I ever learned about that was to make sure that it only comes in for the worst of the Winter, and to keep that stretch as short as possible. I'm expecting about 3 months this year, and I'm already 1/3 of the way there. So far so good.

I'm hoping to seek out an "Arp" rosemary this year, which might well survive outdoors for me.