The verb चुकना is an intransitive verb which literally means something like “to finish (doing something)”.
However, it is most commonly used as a verbal auxiliary. Like most verbal auxiliaries, the main verb appears as a verb stem and is followed by a form of चुकना.
[stem of main verb] [inflected form of चुकना]
All inflection is done upon चुकना since the main verb always appears as a bare stem.
When used as a verbal auxiliary, चुकना has a sense that can be translated into English using the adverb “already”:
क्या आप खाना खा चुके हैं – “Have you already eaten?” / “Have you finished eating?”
मैं अपना काम कर चुका हूँ – “I have already finished my work” / “I finished my work”
मैं रोज़ छह बजे तक काम कर चुकता हूँ – “I finish working by 6 o’clock every day”
मैं कल तक यह किताब लिख चुकूँगा -“I will finish writing this book by tomorrow”