Boil 4 cups water in a medium saucepan. Add salt, then reduce heat to low. Slowly whisk in cornmeal. Cook, stirring frequently, until cornmeal is very thick, about 5 min. Stir in lemon zest and chives. Transfer mixture to an 8 × 8-in. baking dish. Smooth top, then set on a rack to cool, about 1 hour. Cut cooled polenta into 4 equal squares, then cut each square into 4 strips.
Heat a medium non-stick frying pan over medium-high. When pan is hot, add 1 tbsp oil, then 8 pieces of polenta. Fry until tops and bottoms are golden-brown, 4 to 5 min per side. Transfer to a paper-towel-lined plate. Repeat with remaining oil and polenta.