**Core Concept**
The question is testing the knowledge of vaccine contraindications in children with egg allergy. Egg allergy is a common concern in the administration of vaccines produced in chicken eggs or using egg-derived components. The underlying principle is the risk of anaphylaxis or severe allergic reactions to egg proteins present in the vaccine.

**Why the Correct Answer is Right**
The correct answer is the vaccine that contains egg proteins or is produced in chicken eggs. The most common vaccine associated with egg allergy is the influenza vaccine, specifically the trivalent inactivated influenza vaccine (TIV). This vaccine is produced in chicken eggs, and the risk of anaphylaxis or severe allergic reactions is a significant concern in children with egg allergy. The presence of egg proteins in the vaccine can trigger an immune response, leading to severe allergic reactions.

**Why Each Wrong Option is Incorrect**
* **Option A:** The MMR vaccine is a live attenuated vaccine produced in chick embryo tissue culture, but it is not contraindicated in children with egg allergy. The risk of anaphylaxis or severe allergic reactions is low, and the vaccine is generally safe for individuals with egg allergy.
* **Option B:** The Varicella vaccine is a live attenuated vaccine produced in human diploid cell culture, which does not contain egg proteins. It is safe for children with egg allergy and is not contraindicated.
* **Option D:** The Hepatitis A vaccine is produced using recombinant DNA technology and does not contain egg proteins. It is safe for children with egg allergy and is not contraindicated.

**Clinical Pearl / High-Yield Fact**
The risk of anaphylaxis or severe allergic reactions to egg proteins in vaccines is a significant concern, particularly in children with a history of egg allergy. However, not all vaccines are contraindicated in egg allergy, and the risk varies depending on the specific vaccine.

**Correct Answer:** B. Varicella vaccine