We developed a laser interference lithography (LIL) system for fabrication of period-chirped gratings, which would be useful for sophisticated optical components. Despite its simplicity, the developed LIL system, based on a Lloyd's mirror interferometer with a cylindrically concave mirror, can generate chirped gratings, yet over a large area at high throughput owing to the nature of LIL. We have derived exact theoretical equations needed for system design, built the LIL system, and subsequently realized period-chirped gratings. A fabricated sample whose center period is Λ≈600 nm exhibits a continuous period variation of ΔΛ=92 nm across 17 mm width.