Mitosis is the part of the cell cycle whereby the replicated DNA of a non-sexual cell separates and two new daughter cells are formed. In general, there are five different stages to cell mitosis: prophase, prometaphase, metaphase, anaphase, and telophase. You are asking at which stage the chromosomes become visible and the nuclear envelope breaks down. Technically, these events occur in two different stages. The already replicated DNA exists bound with different proteins in a complex called chromatin. During the prophase, the chromatin becomes more tightly coiled and the individual chromosomes begin to appear as discrete units. It is during the beginning of prometaphase, however, that the nuclear envelope breaks down so the microtubules can attach themselves to the chromosomes for eventual separation.
Please note that in older textbooks prometaphase did not exist as a distinct phase on its own. The beginning of prometaphase would have been grouped with the prophase, thus allowing both events to occur within a single phase.