The way one answers this question depends a great deal on how one views the Revelation as a whole. I understand it to be a prophecy of the entire church age from the time of Christ's saving work to his return in glory, described in symbolic terms and with a great deal of recapitulation (or repetition) of themes and events. The major focus of Revelation is the church and her members, rather than the political and social worlds in which we live. Two helpful commentaries which are written from this point of view are Dennis Johnson's Triumph of the Lamb and William Hendricksen's More than Conquerors.
Accordingly, when I read Revelation 13 and 14, I believe the first and second beasts are false religious systems organized to deceive people into counterfeit versions of Christianity. When Revelation 13:16–17 are compared with 14:1, we see that Christians bear the "mark of the Lamb." The implication is that one cannot bear both the Lamb's and the beast's marks at the same time. In Revelation 14:9–11, bearing the beast's mark and worshiping the beast are joined together. Thus, people do not get the beast's mark by accident or unwittingly, but by choosing to worship the beast.
Therefore, I do not believe a Christian can accidentally get the mark of the beast through some sort of medical procedure or tattoo. Furthermore, I believe "the mark of the beast" is a symbolic term for those who have joined a religious system other than biblical Christianity. For these reasons, I do not believe the "verichip" (which I've read about a little on the internet since receiving your question) is the mark of the beast or that Christians should avoid being implanted with it on that account. There may be very good reasons why a Christian would choose not to be implanted with one of these, and those reasons may well be informed by his Christian and biblical view of the world and the human body. However, concerns stemming from Revelation 13–14 should not be among those reasons.
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