Something's wrong with Connie. She's restless. Her limbs move when she doesn't want them to. Her spine jerks when she'd rather just lie down. She's getting thinner. Sounds like a case for some silver bullets and holy water. … or maybe just "a beau," in her father's words. In other words, she still needs to get laid. And guess who's coming to dinner? Michaelis, a horribly vulgar playwright who's got just the thing for Lady Chatterley.
Michaelis may be vulgar, but he's managed to build a successful playwriting career. Clifford puts up with him because he's determined to do whatever needs to be done to be successful himself, including all sorts of "new channels of publicity" (3.9)—we're thinking a Twitter early-adopter.
Connie, on the other hand, actually likes Michaelis because he drags his sense of inferiority around with him.
Okay, so that doesn't sound like an attractive quality, but she likes that he doesn't pretend to be someone he's not. And he's got this vulnerable, wounded kitten side that drives her crazy, in a good way.
Here's an unpleasant reminder of how a lot of people thought back in 1928: our narrator thinks about Michaelis as having the "silent, enduring beauty of a carved ivory Negro mask […] that momentary but revealed immobility, an immobility, timelessness which the Buddha aims at, and which Negroes express sometimes without ever aiming at it; something old, old, and acquiescent in the race!" (3.30). Racism aside (for now), Connie is attracted to him because he's such an outsider. Michaelis has a feeling that he's about to get lucky.
Sure enough, Lady Chatterley invites him up to her sitting room. He spills secrets, talking about his family and laying on the hard-luck story. They flirt in a really melodramatic way, and he finally gets on his knees to hold her hand.
Finally, here comes the good stuff. Aaaaand—it's over in a paragraph. Michaelis walks away and gets all sulky, assuming she's going to be all, "wham, bam, thank you sir" on him. Connie, with some underwhelming pillow talk, insists that she thinks he's "nice" (3.67).
Clifford, however, still can't stand him. Connie makes some excuses for him, and privately thinks that Michaelis's unscrupulousness is kind of hot.
Only he's not unscrupulous with her—he's actually kind of needy, even bringing her a big bouquet of flowers, like, dude, put down the phone and stop texting her six times a day.
She goes to his room again that night, and they have sex again. He finishes too fast, but Connie is able to, you know, finish up afterwards, with his "hard, erect passivity" (3.91). (Sorry. We didn't write it.)
After Michaelis leaves, he writes to her. She writes back and even sneaks away to London for a little afternoon delight once in a while.
It does wonders for her restlessness. She's super cheerful and perky around the house, and Clifford does some of his best writing. Adultery: the cure for the common writer's block.