We present the discovery of a unique object, a chemically peculiar Ap-type star showing delta Scuti pulsations that, is bound in an eclipsing binary system with an orbital period shorter than 3 d. HD 99458 is therefore a complex astrophysical laboratory opening doors for studying various, often contradictory, physical phenomena at the same time. It is the first Ap star ever discovered in an eclipsing binary. The orbital period of 2.722 d is the second shortest among all known chemically peculiar (CP2) binary stars. Pulsations of delta Scuti type are also extremely rare among CP2 stars and no unambiguously proven candidate has been reported. HD 99458 was formerly thought to he a star hosting an exoplanet, but we definitely reject this hypothesis using photometric observations from the K2 mission and new radial velocity measurements. The companion is a low-mass red dwarf star (M_2 = 0.45(2) M_Sun) on an inclined orbit (i = 73.2(6) deg) that shows only grazing eclipses. The rotation and orbital periods are synchronized, while the rotation and orbital axes are misaligned. HD 99458 is an interesting system deserving of more intense investigations.