Step 1: Understanding the Concept
A carbon atom is chiral when it is attached to four different atoms or groups. If any two of its four groups are the same, it is not chiral.
Step 2: Check option (A)
The starred carbon in the first figure carries H, H, Cl and Br and also an unpaired electron dot. It has two identical hydrogens, so it is not a chiral centre.
Step 3: Check option (B)
The starred carbon holds H, \(\text{CH}_3\), OH and I. All four are different, so it is a chiral carbon.
Step 4: Check option (C)
The starred carbon holds two \(\text{CH}_3\) groups, plus Cl and Br. Two identical groups, so it is not chiral.
Step 5: Check option (D)
The starred carbon holds H, Cl and two \(\text{C}_2\text{H}_5\) groups. Two identical ethyl groups, so it is not chiral.
Final Answer:
Only the carbon with H, methyl, OH and iodine has four different groups, option (B).
\[ \boxed{\text{(B)}} \]