ㄹ리 없다, which is more natural than ㄹ이유없다, is more formal than ㄹ 턱이 없다. 턱걸이 is related to the sports of horizontal bar. You could catch the meaning of 턱이 없다 from the following example sentences. 1) 간신히 턱걸이했다.(=He did chin-up the bar barely.) 2) 대학시험에 간신히 합격했다.(=He passed the entrance examination of the university. Perhaps he is the last rank among the passed students.) [=대학시험에 턱걸이로 합격했다.] 3) 그가 예일대에 합격할 턱이(리) 없다.(It is unreasonable he entered Yale University.) 4) 그녀가 그런 사람을 사랑할 턱이(리) 없다.(There is no way she would love such that man.)