The existence of old high-redshift objects provides an important tool for constraining the expanding age of the Universe and the formation epoch of the first objects. In a recent paper, Hasinger {it et al.} (2002) reported the discovery of the quasar APM 08279+5255 at redshift $z=3.91$ with an extremely high iron abundance, and estimated age of 2 - 3Gyr. By assuming the lower limit for this age estimate and the latest measurements of the Hubble parameter as given by the HST key project, we study some cosmological implications from the existence of this object. In particular, we derive new limits on the dark matter and vacuum energy contribution. Our analysis is also extended to quintessence scenarios in which the dark energy is parameterized by a smooth component with an equation of state $p_x = omega_x rho_x$ ($-1leq omega_x < 0$). For flat models with a relic cosmological constant we show that the vacuum energy density parameter is constrained to be $Omega_Lambda geq 0.78$, a result that is marginally compatible with recent observations from type Ia supernovae (SNe Ia) and cosmic microwave background (CMB). For quintessence scenarios the same analysis restricts the cosmic parameter to $omega_x leq -0.22$. Limits on a possible first epoch of quasar formation are also briefly discussed. The existence of this object pushes the formation era back to extremely high redshifts.