Phono-semantic compound (形聲, OC *sn̥ʰiːn): semantic 一(“one, signifying a number”) + phonetic 人(OC *njin). The Old Chinese pronunciations of 千 (OC *sn̥ʰiːn) and 人 (OC *njin) were similar. For the component 人, compare its combining form 亻.
The traditional explanation holds that the extra line indicates an extension (see the etymologies of 年 and 延). 千 has the meaning one thousand because one thousand is a number that is reached by extending one's counting.