We have $\varphi(1000)=400=2^4\times 5^2$. Therefore, it is sufficient to check all the divisors of $400$.

• $17^{200}\equiv 1\pmod{1000}$
  
• $17^{100}\equiv 1\pmod{1000}$
• $17^{50}\equiv 49 \not\equiv 1\pmod{1000}$

Therefore, the answer is $\boxed{100}$.