Eternal security (and it's corollary OSAS) is entirely Biblical, as well as soundly Christian.
"They, whom God hath accepted in his Beloved, effectually called, and sanctified by his Spirit, can neither totally nor finally fall away from the state of grace, but shall certainly persevere therein to the end, and be eternally saved. This perseverance of the saints depends not upon their own free will, but upon the immutability of the decree of election, flowing from the free and unchangeable love of God the Father; upon the efficacy of the merit and intercession of Jesus Christ, the abiding of the Spirit, and of the seed of God within them, and the nature of the covenant of grace: from all which ariseth also the certainty and infallibility thereof. Nevertheless, they may, through the temptations of Satan and of the world, the prevalency of corruption remaining in them, and the neglect of the means of their preservation, fall into grievous sins; and, for a time, continue therein: whereby they incur God's displeasure, and grieve his Holy Spirit, come to be deprived of some measure of their graces and comforts, have their hearts hardened, and their consciences wounded; hurt and scandalize others, and bring temporal judgments upon themselves." Westminster Confession of Faith [17]
"Since you have been born again, not of perishable seed but of imperishable, through the living and abiding word of God."
1 Peter 1:23
"All that the Father gives me will come to me, and whoever comes to me I will never cast out."
John 6:37
"My sheep hear my voice, and I know them, and they follow me. I give them eternal life, and they will never perish, and no one will snatch them out of my hand. My Father, who has given them to me, is greater than all, and no one is able to snatch them out of the Father's hand."
John 10:27-29
"Who shall separate us from the love of Christ? Shall tribulation, or distress, or persecution, or famine, or nakedness, or danger, or sword?"
Romans 8:35
"For I am sure that neither death nor life, nor angels nor rulers, nor things present nor things to come, nor powers, nor height nor depth, nor anything else in all creation, will be able to separate us from the love of God in Christ Jesus our Lord."
Romans 8:38-39
"For the gifts and the calling of God are irrevocable."
Romans 11:29
"They went out from us, but they were not of us; for if they had been of us, they would have continued with us. But they went out, that it might become plain that they all are not of us."
1 John 2:19
"And I am sure of this, that He who began a good work in you will bring it to completion at the day of Jesus Christ."
Philippians 1:6
"If we are faithless, he remains faithful - for he cannot deny himself."
2 Timothy 2:13
Need I go on?