The can and likely will produce peppers indoors during the winter. Mine do but much less prolifically than during the summer and outdoors. I ate several nice ripe pods off my Hot Hungarian Wax this past winter. Here is a photo of my HHW with a pod on it from March of this year.
Bruce

YEP..
I over wintered a Jalapeno for the first time and so far have eatten 2 off of it and now have another two pods starting out.

Flowered quite a bit but I had picked most of them off so it would put its focus on growing before pushing peppers.

I haven't overwintered any plants yet, but I can confirm that both Jalapeños and HHW are more than willing to put on fruit indoors. I've had plenty of pods on those kinds since April (plants where sown in February). I would assume overwintered plants would do something similar.

Bruce: Do you keep the overwintered plants under artificial lighting during the winter, or just near a window?

I've still been unsuccessful at overwintering(meek attempts) but mine are still going strong into the winter here anyhow. However, one thing people should take into account -- winter pods lose much of their HEAT. Still tasty, but far less hot.

Margowicz: you could probably do it with tomatoes also, but tomatoes are far more susceptible to disease, it may not be worth it. There are varieties like Glacier and Kodiak that produce at lower temps.

Kevin

I was into knowing so I could get a GH going it might not be this year but I think I should have one next year I also need experiment with compost mixes

I will try wrap some fleece around the pot see I didn't want to go threw the hassle of a GH if it would not fruit.... I am not into the heat i want the taste from them and want try all types tabasco is one I love the colorful chillies.

I know the chillies I can take the seed plant them but is there any types of seed I should look to start something like F1 seeds...

Thank to guys

It depends on the amount of light and warmth they get.

It's not uncommon to get a few fruit over the winter, but, sometimes you don't.

cjohansen: This is the second winter that I had overwintered that particular plant. I don't put it under lights but keep it near a SW facing window that get some direct light but not much. I prune them back quite a bit and it takes a long time to recover from that. I am not sure if they would produce better if I left them alone after bringing them in or not. As far as the lower heat issue goes, I am not a fire eater so that is fine with me. If I wanted hotter peppers over the winter, I would simply overwinter a hotter variety I guess.
Bruce

It depends on the plant. I overwintered 6 tabascos with branches pruned back by 2/3. One plant was prolific, one died, and the rest were in between.

You must not have searched very hard for this information....this took about 5 sec.

http://search.gardenweb.com/search/nph-ind.cgi?term=overwintering&forum=pepper&forum_name=Hot+Pepper

Wrong link, this is the one

http://search.gardenweb.com/search/nph-ind.cgi?term=overwintering&forum=pepper&forum_name=Hot+Pepper

look at what it says before you come on it says HOW DO YOU OVER WINTER CHILLIES I(me) asked DO YOU GET CHILLIES IN THE WINTER

The tite says.........:over wintering chillies