Python 2.7 String Index Error

I'm writing a program to choose a random line from a text file using a while loop as a counter and then another variable to choose the random line:

import random 


fortunes_file = open("fortunes.txt", "r")


fortunes = fortunes_file.readline()

count = 0


while fortunes != "":
    count += 1
    fortunes = fortunes_file.readline()

rand_line = random.randint(1, count)

print fortunes[rand_line]

fortunes_file.close()

However, I get the following error when trying to run the program:

IndexError: string index out of range