Relationships
Given that Tales of Phantasia was originally created for the Super Nintendo Entertainment System, like most other SNES games, character interactions are limited to today's standards for the most part. Overall, there are two major relationships that Chester has with the other playable characters in this game.
Cress Albane
Cress and Chester are childhood friends, and it is clear that they trust each other completely, though for Chester to sacrifice himself to distract Dhaos so that Cress and Mint may go back into the past and wait dutifully for them. In the game, it is Cress who insists that Chester rejoins them once they return to the present, though in the Animation it is Chester who insists on tagging along, in spite of his injuries.
Chester views his relationship with Cress as a barometer of sorts for himself; since they were always training together, they were on equal ground for the majority of their lives. However, by Chester's own choice to stay behind to help Cress by distracting Dhaos, Cress returned moments later with several levels of experienced increased, and was now far more powerful than Chester.
This frustrated Chester, because they were no longer on equal footing. He couldn't very well take out this frustration on Cress, because it was Chester's own decision to help him out this way. In both the game and the Animation, Chester undergoes private training in the middle of the night in order to gain experience; in the game, this allows him to gain several levels.
It is also obvious that Cress cares a lot about Chester as well, since in the game Cress was in possession of Chester's broken bow during his time in the past. Refusing to get it replaced, he asked the elves in Heimdall to help repair it, and was directed to Arsia. If this side quest is taken (a quest only available in this form in the GBA and PSP remakes), you are basically set for Chester's weapons since shortly after you return to the present, you can get the Elven Bow, and with a few more events, you gain Chester's most powerful weapon, the Elven Bow 2.
Arche Klein
Arche is an interesting character in herself, and you can tell that she was a favorite of the staff since she receives much attention and development, from being turned to stone to being not allowed to enter Heimdall. She's spunky, and according to Claus, "she's a firebrand" (players of the DeJap fan translation may remember this line by a more memorable wording). In the Animation, she even gets very interested in Chester as Cress keeps on talking about him.
Of course, once she actually meets him, she feels that he's a letdown. In both the game and the Animation, Arche follows Chester outside during one of his self-training sessions, though in the Animation she more gets on his nerves than is there to keep him company. Also, despite the initial bad terms, Arche makes no hesitation to overhear a hot springs conversation with the topic being Chester's body, and promptly proceeds to attempt peeping. In an earlier hot springs scene, she is the one who labels Chester as a "Bad Boy" for his libido. Throughout the game, Arche subjects Chester to comments to make him feel inferior.
The two are very different, as well, and complement each other well in this regard in both design and personality. For instance, their color schemes are opposite, blue and pink. Chester is a melee attacker, while Arche is a mage. Chester is more traditional and probably conservative, while Arche is definitely progressive and mostly liberal in attitude.
Despite the antagonism between these two, it's fairly obvious that the saying "good friends always fight" is given some merit, as eventually it is made obvious that the two care about each other. An added scene in the Animation shows Chester leaving Heimdall in favor of keeping Arche company in the rain. Later on, the two are paired off during the team's stay ar Arlee; once again, in the Animation, hints are shown that they actually like each other, as Chester confronts Arche and tells her that he's willing to travel back and live with her in the past. Arche, of course, declines ("What the mystery to me is, can any guy from any time stand you?") and later on goes to say that they'll meet in a century, anyhow.