A.
In any zone in which a one-family dwelling is permitted, a one-family dwelling and customary accessory buildings may be erected on any single lot of record at the effective date of adoption or amendment of this chapter creating the nonconformity, provided:
(1)
Such lot was a valid, lawfully existing lot prior to the adoption or amendment of this chapter which created the nonconformity; and
(2)
The nonconformity of the lot relates to size or area; and
(3)
All other provisions of this chapter, including yard requirements, are complied with, or a variance from such compliance has been obtained from the Board of Appeals.
B.
In addition, upon receipt of a special approval from the Board of Appeals, a two-family dwelling may be constructed on such a lot if permitted by the regulations of the zone, subject to the conditions set forth above, and subject to any conditions (such as occupancy or dwelling unit size) that govern two-family dwellings in the zone in which the dwelling is located.