First sterilise a jar large enough to hold all six eggs. Either run it through the hottest setting in your dishwasher, or wash in plenty of hot, soapy water, rinse thoroughly, then put in a low oven to dry out completely.
Bring a saucepan of water to the boil, then gently lower in the eggs. Boil for 7 minutes exactly, then remove from the heat, strain, and run under cold water to stop them cooking. When they are cool enough to handle, peel carefully.
Put the cider vinegar in a saucepan with 150ml/5fl oz water, salt and sugar. Slowly bring to the boil, stirring to dissolve the sugar, then simmer for 5 minutes. If using the chilli, add this at the last minute.
Pack the eggs into the jar, then pour over the vinegar mixture. Seal and leave to cool completely. Leave for at least 2 weeks before eating, preferably a month, then store in the fridge once opened.