ANSWER: 1

EXPLANATION:
Looking at the consecutive powers of seven, starting with one, we see that the unit's place of 71 = 7, 72= 49, 73= 343, 74 = 2401, and 75= 16807. Looking at just the unit's place, we have the repeating series 7,9,3,1,7,9,3,1..., which repeats every 4 numbers. Since 1000 is divisble by 4 (the cycle length), the 1000th term of this series is the same as the fourth term, which is 1.