You need not chase the 'I am' to kill it. You cannot. All you need is a sincere longing for reality. We call it atma-bhakti, the love of the Supreme: or moksha-sankalpa, the determination to be free from the false. Without love, and will inspired by love, nothing can be done. Merely talking about Reality without doing anything about it is self-defeating. There must be love in the relation between the person who says 'I am' and the observer of that 'I am'. As long as the observer, the inner self, the 'higher' self, considers himself apart from the observed, the 'lower' self, despises it and condemns it, the situation is hopeless. It is only when the observer (vyakta) accepts the person (vyakti) as a projection or manifestation of himself, and, so to say, takes the self into the Self, the duality of 'I' and 'this' goes and in the identity of the outer and the inner the Supreme Reality manifests itself.