The simple answer is, maybe. But if so, we do not have evidence from Bible prophecy.
The idea of microchips is based on speculation concerning the Mark of the Beast: “He (the beast from the Earth) causes all, both small and great, rich and poor, free and slave, to receive a mark on their right hand or on their foreheads, and that no one may buy or sell except one who has the mark or the name of the beast, or the number of his name” (Revelation 13:16,17).
We should notice first that the Mark seems to be very closely related to the Name and Number of the beast. It appears that either the mark or the number of the beast could be used to prevent someone from buying or selling. Τhe next verse makes it clear that the original readers of Revelation would have the ability to understand the Number of the beast, and presumably the Mark as well— “Let him who has wisdom calculate the number of the beast” (v. 18). Obviously that would rule out modern high tech innovations (such as microchips) as being the primary explanation of the Mark and Number of the Beast.
However, within the prophecy is a key that would make it understandable to the original readers who were familiar with the scriptures: the mark was to be on their right hand or on their foreheads. The first century Christian readers of Revelation would have certainly remembered that Moses told the children of Israel, “Obey my commandments which I command you today… You shall lay up these words of mine in your heart and in your soul, and bind them as a sign on your hand, and they shall be as frontlets between your eyes” (Deuteronomy 11:13, 18, 6:8). In these verses we see that it is God’s commandments that were to be a sign, bound to their hand or forehead. Although ultra-orthodox Jews have taken this commandment literally and made little boxes with a copy of the law inside and fastened them to their wrists and on their foreheads, the real issue is “in your heart and in your soul”.
In the new covenant God promises, “I will put My laws in their mind and write them on their hearts” (Hebrews 8:10). From the heart proceed thoughts (symbolized by the forehead) and actions (symbolized by the hand). From this text in Deuteronomy we can assume that the beast (the agent of Satan) will try to replace God’s laws with his laws, and his antichrist laws will be reflected in the minds and hearts (forehead), or at least in the actions (hand) of those who submit to the beast.
This explanation is in harmony with the prophecy of Daniel 7:25, which shows that the agenda of Satan is to change God’s law: “He (the little horn, who is the agent of Satan) shall speak pompous words against the Most High, shall persecute the saints of the Most High, and shall intend to change times and law. Then the saints shall be given into his hand”.
The law Satan “intends to change” is the law of God. Just as with the Mark of the Beast, Satan tries to force God’s followers to yield to his authority. His purpose is to show first of all that his authority over mankind is greater than that of God, since man obeys his laws rather than God’s. Secondly, he seeks to show that God’s law can be changed, because the law of God condemns him as a sinner. Third, he seeks to force God’s followers to become lawbreakers; then he can insist that if God allows them to live, He must allow him to live too.
Satan cannot really change God’s law; this is why the verse says that “he shall intend to change times and law”. It is also obvious that a direct attack on the Ten Commandment law would be counterproductive, since most of the points (“You shall not murder… steal… commit adultery etc.) are in the public interest and generally supported by society.
Therefore Satan will make subtle, clever changes in God’s law, knowing that “whoever shall keep the whole law, and yet stumble in one point, he is guilty of all” (James 2:10). The Mark of the Beast will be the modified law of God that Satan, through his agent the beast, will try to enforce on the whole world.
If microchips will be used at all, they will be a secondary issue, or more probably, a distraction by Satan to deceive people so that they do not discern the real issues. They will accept the Mark of the Beast while refusing a microchip.
The issue of the Mark and Number of the Beast is of vital importance but requires more scriptural support than a short article can provide. To find out what they are please take the time to read chapter 13 of The Book.