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Scrub potatoes and cut into bite-sized chunks.
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Boil water in a medium-sized saucepan; add a bit of salt to the water, and then potatoes. Return to a gentle boil, then lower heat and simmer for 10-15 minutes, until potatoes are just tender when pierced with a sharp knife. Drain and let cool until they can be handled.
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Mash garlic clove with 3/4 teaspoon salt in a mortar and pestle until a paste forms. Put olive oil in a mixing bowl and gradually whisk in lemon juice. Whisk in the garlic paste and paprika.
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When potatoes can be handled, peel them (this is optional if the skins are thin). Peel the chilli and chop it into bits. Place potatoes and chilli in a serving bowl. Drizzle dressing over top and mix gently. Serve warm or cold.