i-adjective
Describes a situation, group, or process that is well-organized and follows proper order. Often used for meetings, queues, or systematic arrangements.
会議は秩序正しく進められた。
The meeting was conducted in an orderly manner.
彼らは秩序正しく列に並んでいた。
They were lined up in an orderly queue.
きちんと is a common adverb for doing things properly or neatly. 秩序正しい is a more formal adjective describing the state of being orderly.
Compound of 秩序 (order) + 正しい (correct, proper). The exact historical derivation is uncertain, but the combination naturally yields the meaning 'orderly'.