Are antibiotics necessary for the treatment of a hordeolum?

Usually not.  Hordeola which are caused by obstruction of the oil-producing meibomian glands tend to be self-limited and often resolve spontaneously within a week or perhaps earlier with the frequent application of warm compresses.

Although there have been no clinical trials to prove benefit, topical antibiotics are recommended by some sources to - in theory - prevent secondary infection of other meibomian glands.  Systemic antibiotics should be administered for secondary cellulitis.


Source

Ferri: Ferri's Clinical Advisor 2011, 1st ed.

Greenberg, M.  "Diagnosis: A Hordeolum"  Emergency Medicine News.  2002 June.

Lindsley, K.  et al.  "Interventions for acute internal hordeolum."  Cochrane Database Syst Rev.  2010 Sept.

Wald, ER.  "Periorbital and orbital infections"  Infect Dis Clin North Am.  2007 June.

Yanoff & Duker: Ophthalmology, 3rd ed.