Tica,
I would either contact the fellowship or have your Chief contact the fellowship and clarify exactly what it is they are requesting. A program cannot provide a letter of board eligibility, only the ABOS can provide such a letter as a candidate is not considered board eligible until they sit and pass Part I of the ABOS examination. A program can state that the resident has met all educational requirements or is on track to meet all educational requirements established by the ABOS and has registered to take Part I. The fellowship should provided clarification on exactly what they are requesting and should be aware that a residency program cannot provide a statement on board eligibility.
Cindy