For a definitive answer, please link to the card that you are buying. If it is the VTX3D HD 7870 Black Edition, then yes; you can. The VTX HD 7870 is based on the Tahiti LE core, which the HD 7950 and HD 7970 are based on. So you can CrossFireX the HD 7870 with a HD 7870 XT, HD 7950, or HD 7970. That also means you can CrossFireX it with other rebranding of those cards.
If it is NOT that card, then it's up in question. If you can provide the link to it, it would help.
P.S.: unselecting the best answer. I'll leave that to @xalyy.