"Many hash table designs also allow arbitrary insertions and deletions of key-value pairs, at constant average (indeed, amortized) cost per operation." -- http://en.wikipedia.org/wiki/Hash_table

"Hash tables, sometimes also known as associative arrays, or scatter tables, are a data structure that offers fast lookup, insertion, and deletion of (key, value) pairs. In a well-designed implementation of hash tables, all of these operations have a time complexity of O(1), rather than the O(n) that linked lists, association lists, and vectors would require for some of them." -- http://www.math.utah.edu/~beebe/software/hash/hash.html

I'll grant that an individual lookup might consume greater than O(1) time, but in the aggregate it's fairly well established and accepted that hash operations are O(1) operations, where 'n' is the number of elements in the hash.