Python 3.8 (pre-release), 37 bytes

def f(l,i=0):  while 1:print(i:=l[i]) 

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Python 3.8 (pre-release), 37 34 bytes

def f(l,i=0):print(l[i]);f(l,l[i]) 

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thanks user for helping save 3 bytes

slightly modified version of 31 bytes, but it prints an extra zero at the beginning

def f(l,i=0):print(i);f(l,l[i]) 

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Python 3, 66 bytes

def f(l): a=l[0],l[l[0]] while a[0]-a[-1]:a+=l[a[-1]], return a 

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Python 3.8 (pre-release), 37 bytes

def f(l,i=0): while 1:print(i:=l[i]) 

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