Eternal security? Yes, indeed.
Romans 11:29
For the gifts and calling of God are without repentance.
Romans 6:23
For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
The word "repentance" found in 11:29 in Greek means "irrevocable." The definition of irrevocable is unchangeable, irreversible, unalterable, etc.. We know from 6:23 that one of God's gifts is eternal life so, therefore, it cannot be taken away from us.
Can we cause ourselves to lose it?
Romans 8:38-39
For I am persuaded, that neither deather, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.
From this verse it is very clear that NO CREATURE or anything else could separate us from God's love. We cannot separate ourselves from Him.
Why?
Jude 24-25
Now unto him that is able to keep you from falling, and to present you faultless before the presence of his glory with exceeding joy, To the only wise God our Savior, be glory and majesty, dominion and power, both now and ever. Amen.
We don't have to keep ourselves from falling because He can do that for us.