I make lots of chutney, but I am afraid it is all sweet. Chutney relies on sugar and vinegar as preservatives, so although you can find low carb chutney recipes such as this one
you have to keep it in the fridge and use it up pretty quick, you can't "mature" it like you can with a chutney made with sugar.
We had a bumper crop of pears off our tree this year, so I made 26 jars of spiced Pear and Ginger chutney, which will get spicier the longer you keep it (4 or 5 finely chopped chillies with seeds went into it). I tend to give a lot away, but I'll have some with cold meats or cheese from time to time. Since I only use about a teaspoon full at a time I tend not to worry about it.