This is a pretty compact and - I think - easy to read way of doing it:
while(display != list(chosen_word)):
guess = input("Guess a letter: ").lower()
display = list(map(lambda c, d: c if d != '_' or c == guess else d, chosen_word, display))
print(display)
print("Congrats! You did it!")
Mapping over an array is a pretty powerful tool and also using ternary expressions. If you're not familiar, a map basically just iterates over an array and runs a function on that item, replacing it with whatever the return value of the function is.