roof repair referral needed

Sounds like the seal is not tight enough around the chimney. This should be an easy repair, just install a new flashing around he chimney and seal it.

If you ignored the problem for an extended amount of time, the water may have damaged the baseboard under the shingles. They should be replaced or it will continue to rot.

This type of problem should be addressed immediately.

Yep - the flashing will need to be repaired.

Note - depending on the chimney, the old flashing probably won't need to be replaced with new flashing but just re-positioned so that it covers the holes again. Over time, the metal flashing bends due to snow load and ice so that they may not be in the right position to their job, Many older chimneys have the flashing sandwiched between the courses of brick so replacing the flashing will mean removal of mortar and maybe bricks which is a big job. So, look for someone who understands this and will go for a re-positioning of the flashing instead.