The defender, who is yet to make his first team debut for the Spireites, has played for the reserves this season, and scored against Scunthorpe United reserves last week.
Graham, 23, came to the Proact on trial and joined the club in October.
A New Zealand Under 20 international, he joins a Whitehawk side sitting 15th in National League South.
The Brighton club’s greatest success this season came in the FA Cup, beating Lincoln in the first round proper and taking Dagenham and Redbridge to a replay in the second round, before a 3-2 defeat.
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Graham’s loan spell has been set at 28 days initially.