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I have a Zimbabwean Black chilli plant on my kitchen window sill. It is covered in flowers but they just die & fall off. They don't produce any fruit.

What am I doing wrong?

Thanks.

Geri

How bit is your plant?
How big is the pot?
Do you feed your plant and what with?
Does it get much sun light?
Does it get hot on the window sill?
Is you plant otherwise healthy?
Does the flowers actually open up before falling off?
Do they fall off with stalks on or just the actual flower?

There is some many things that can influence for flower drop...but usual reasons would be plant getting too hot, to dry/moist air so that the flower doesn't get pollinated or compost drying out too much.
If it has energy to flower a lot...there should be enough food going in...but does it get right kind of food for able to grow the fruit?..and would be supply of potash..

If it happens to me I often reach for the water sprayer to see if it will help with setting the fruit.