Frost bitten chilli plant

[clairebear]

We tentatively ventured into the world of chilli's a couple of weeks ago and bought a Habanero chilli plant which I promptly put outside following a bit of reading on the web. Turns out I was a bit too keen as we started a week long spate of frosts and I was a bit lax and left the poor little beastie outside. Fetched it back indoors the next day very obviously frost damaged, blackened leaves and the very tip of the stalk has also gone black.
This was around a week and a half ago. We've pulled all the dead/dying leaves off but left the stalk intact.
This morning though I've noticed what look like new, green leaves having a go at survival but the stalk looks like it's rotting at the top, sort of a grey/black colour and what almost looks a little mouldy. Seeing as we seem to have signs of life I'm not sure whether to nip the top off or leave it and if I do nip the top where should I cut it?
Any help on this would be great

[rustylady]

Cut the top off below the discoloration. Keep the plant indoors for now and keep an eye on it. Don't overwater it.

[Two_Sheds]

You need to cut off any dead or dying tissue, because otherwise rot will travel to the rest of the seedling

[northepaul]

If you are going to put chillis outside, it might be worth waiting until at least a month's time (or until well after the frosts have finished.) Personally I dont put them outside at all.