Atomic and nuclear properties of positronium (Ps):
Positronium (Z = 1 atom with e⁺ as nucleus)

Quantity	Value	Units	Value	Units
Atomic number	1	n	n	n
Mass*	1.097 526 752 (5)	10-3 u	1.021 991 03 (9)	MeV
Mean lifetime (annihilation)	Singlet (p-Ps): 125 (Predominately Ps→2γ)	ps	Triplet (o-Ps): 142.05 ± 0.02 (Predominately Ps→3γ)	ns

* Ground state binding energy = Ry/2.

Is it reasonable to consider Ps as a chemical element?

• It is bound electronically. If we consider atoms as having orbital electrons,
  then the positron plays the role of nucleus.
• It has a rich chemistry, as Google searches on "positronium halides,"
  "positronium compounds," and other strings show. There are international
  conferences on positronium chemistry.
• In other exotic atoms such as muonium, pionium, and kaonium, the bound
  muon or meson plays the role of an orbital electron instead of being the
  nucleus. Although e⁻π⁺ and other such atoms might equally well be
  regarded as elements, as would atoms with hypernuclei, these contain
  unstable particles. An isolated positron is presumably as stable as an electron.
• One serious objection is that the positronium "nucleus" has non-zero lepton
  number. (e⁻π⁺ and atoms with hypernuclei have nuclei with lepton number
  zero, as do "normal" nuclei.)
• We are physicists, not chemists.