Brighton-based Hawks are semi-professional and play in the Vanarama National League South, two divisions below their full-time opponents.
They are the last team in Sussex left in the competition other than Brighton & Hove Albion.
The two League Two clubs drew 0-0 on Saturday and will be playing a replay on a date to be confirmed.
The second round matches will be played over the weekend of December 5-6.
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