Combine the carrots, cucumbers and onions in a medium bowl
In a saucepan, bring the vinegar, granulated sugar, salt, peppercorns and chile to a boil.
Turn down the heat and let it simmer for 3 minutes.
Turn off the heat and let it cool for 5 minutes.
Pour over the vegetables and toss to coat. (I discarded the chile before doing this to keep the heat down).
Cover and refrigerate for at least 1 hour. The mixture will keep, chilled in the brine, for 1 week.