Sure, I can help you write a test case generator for the "Tournament Chart" problem. Here is a Python function that generates random test cases for this problem:

```python
import random
import string

def generate_tournament_chart(contestants):
    """
    Generates a balanced tournament chart for a given list of contestants.
    """
    if len(contestants) == 1:
        return contestants[0]
    mid = len(contestants) // 2
    left_chart = generate_tournament_chart(contestants[:mid])
    right_chart = generate_tournament_chart(contestants[mid:])
    return f"[{left_chart}-{right_chart}]"

def tcgen():
    N = random.randint(2, 26)  # Number of contestants (2 ≤ N ≤ 26)
    
    # Generate unique contestants
    contestants = random.sample(string.ascii_lowercase, N)
    
    # Generate tournament chart
    S = generate_tournament_chart(contestants)
    
    # Generate win counts for each contestant
    wins = {contestant: random.randint(0, N - 1) for contestant in contestants}
    
    # Format the output
    result = [S]
    for contestant in contestants:
        result.append(f"{contestant} {wins[contestant]}")
    
    return "\n".join(result)

# Example usage:
print(tcgen())
```

### Explanation

1. **generate_tournament_chart(contestants):**
   This recursive function generates a balanced tournament chart for a given list of contestants. It splits the list into two halves, recursively generates the tournament chart for each half, and then combines them into the required format.

2. **tcgen():**
   - **N:** Randomly chooses the number of contestants between 2 and 26.
   - **contestants:** Randomly samples `N` unique lowercase letters to represent the contestants.
   - **S:** Uses the `generate_tournament_chart` function to create the tournament chart.
   - **wins:** Randomly generates a win count for each contestant.
   - **result:** Formats the output as required by the problem statement.

You can run the `tcgen()` function to generate a random test case for the "Tournament Chart" problem. The function prints the tournament chart followed by the win counts for each contestant.