Connected:

GORE
SORE
SORT
PORT
PART
PERT
PEST
TEST
TEAT
TEAL
DEAL
DEAN

Or as animation:

NOTE: We're not particularly happy with some of the words in the chain (e.g. TEAT, PEST, SORE) but we did this in a hurry, and it's not easy to find words to make the transition between a consonant-vowel-consonant-vowel word (GORE) and a consonant-vowel-vowel-consonant word (DEAN) in single-letter steps.

UPDATE: We were pretty sure this post would generate some responses, and it did. A better chain was suggested by:

Kevin GORE GONE DONE HONE HOPE HOSE LOSE LOST MOST MOAT BOAT BEAT BEAM BEAD LEAD LEAN DEAN

Phil GORE PORE PORT PERT PEAT BEAT BEAN DEAN

Michael GORE TORE TORT TOOT LOOT LOON LOAN LEAN DEAN

John (computer assisted!) GORE MORE MORN MOAN LOAN LEAN DEAN

Peter (these are dictionary words) GORE LORE LORN LARN DARN DERN DEAN